Where is the most densely populated square kilometre in the UK?

After the recent release of England and Wales Census data for 2021 I decided to take a quick look at which areas have the highest population density. I've done this kind of thing before, for the whole of Europe and also in relation to thinking about measures of population density more generally - in short, my view is that using the arithmetic mean approach to density makes very little sense at the country level because it doesn't reflect how we actually experience density (unless we live somewhere like Monaco). That's why I came up with the very simple idea of using 'lived density' instead. But this piece is about my attempt to find the area of the UK with the highest population density in a single square km. And note that I say 'in the UK' in the title because the highest density area of the UK is within London - the highest densities in (e.g.) Glasgow, Edinburgh, Cardiff or Belfast are about half that of London's densest areas. Here's where I think the most densely populated square kilometre in the UK is, based on 2021 Census data.

This is the answer to my question - read on to see how I got here

Here's a map of the southeast of England (mostly) showing 1km density - brighter colours = higher density. There are a few very high density areas outside London, but not necessarily exactly where you might expect.

No big shock to find London has the highest densities

That London has the highest population density areas of the whole UK is not a surprise. Previously my calculations on the highest population densities in London led to figures in the range of 20,000 to 25,000 people in a single square km. But of course this refers to residential density, and my previous calculations arrived at a figure of about 120,000 people in a single square km for daytime population density (see below, where the top figure is daytime population and the bottom figure is residential).

Daytime density in parts of Central London is over 100,000 per sq km

The centres of cities such as Manchester and Birmingham in particular have some pretty high densities - over 10,000 per sq km - but London has by far the highest density and the largest number of areas above 15,000 per square km in relation to residential population density. If you're interested in daytime (i.e. workday) population density then I wrote about that in a previous post.

Okay, so where was I? Yes, trying to find the single square km in the UK with the highest population density. I can say UK with some confidence even though I'm only using data for England and Wales, like I've already said, because my previous analysis shows that the answer is definitely in London.

How do we estimate where the highest density is?

First of all, we attach the output area population data from the 2021 census to the 2021 output area boundaries and we get something pretty uninspiring, like the basic map below. There are over 180,000 output areas and they are quite small. This was all done in QGIS, but I've not really bothered trying to make it look pretty here because I just wanted to find the answer.

All output areas, with 2021 population data

Then we create a 1km grid that covers all of England and Wales. At this point I should point out that the answers you get when doing any kind of 'per sq km' calculation do of course depend upon where you draw your grid Shift it a little up or down, or left or right and you will obviously get slightly different results. But not radically different numbers (as we'll see later on). Also, if you're using output areas to do population density calculations - instead of a 1km grid - then your numbers won't make a lot of sense because the vast majority of them (90%) are under 1km in size. 

In fact, most output areas are tiny, as in the example from the Isle of Dogs in London (below), where we see one output area with a density figure of over 142,000 people per square km - but of course it's WAY smaller than a square km, which are illustrated with the big black lines and the big numbers. Using a population density figure like this would make no sense. This stuff is pretty obvious but sometimes people quote these kinds of figures without realising how small output areas actually are.

Dense? Yes. 140,000 per sq km? No.

Once I had the 1km grid overlaid on England and Wales I think used population-weighted centroids for the output areas and assigned them each to a single 1km grid square and then added up the total population in each. This is of course not perfect because output areas don't align perfectly with the grid but it's close enough in the areas of interest to take us closer to a plausible answer. Here's what that looks like in part of Manchester and Birmingham - messy maps but you get the point. The big numbers are the 1km cell populations and the small numbers are the output area populations.

Central Manchester wasn't like this 20 years ago

This rivals parts of London for density

Okay, so what next? Well, next was to filter for all those square km with more than 15,000 people. Bear in mind that at this stage we are still talking in rough figures because of the mismatch between output area boundaries and the grid - an example of this is shown below but you can see it's not a terrible fit - only those output areas with their population-weighted centroid within the 1km square are added to that square's total. So the overlapping ones with most population outside are assigned to a neighbouring square. Again, not perfect, but logical. The big numbers here are the population in each square - with only squares with more than 15,000 shown and labelled.

This is just of City Road in London

Surprised by the grid squares I found (below) that have more than 15,000 people? I did think Manchester would crack this list but not based on the 1km grid I used. Apart from that it's mostly what I'd expect. There's one square in each of Leeds, Birmingham, Leicester and Brighton and 63 in London. You might get some others in other places if you were to shuffle the grid around a bit. For example, I tried this in Portsmouth (a relatively very dense city) where the highest values on my 1km grid were approaching 14,000 per sq km. I managed to get a figure of 15,509 in a single square km by manually placing the square somewhere else (see below). But in these cases no matter what you do you're not going to reach London densities.

Portsmouth is a very dense city for the UK

The 67 1km squares with more than 15,000 people

Here are some zoomed-in versions showing the location of the highest density 1km squares across England (it's likely that these are also the highest in the whole UK, given that when I last did this Glasgow and Edinburgh had max densities of about 12,000 in any single square).

This is the Birmingham one

This is the Brighton one

This is the Leeds one

This is the Leicester one, to the east of the train station

The 63 London 1km squares, with population labels

Okay, get to the point mate

Run another filter and this time do it for over 20,000 in any single square km and what do you get? You get the map below, with three possible candidates for 'most densely populated square km in the UK'.

These areas all seem like plausible answers to my question

See below for the zoomed in versions showing more detail. The reason they are tilted slightly in this one and the maps above is because I changed the map projection so that the OpenStreetMap layer (© OpenStreetMap contributors) is nice and crisp because if you show it using the British National Grid projection it comes out a bit fuzzy, that's all. 

Notice London Marylebone in the square here

Bow Common Gas Works in the centre here

This area is around Upton Park

Okay, so which square should we choose as 'most densely populated'? Is it a case of just taking the one with the highest population figure? Maybe, but I wanted to investigate more first. In each case there are overlaps around the edges of the 1km squares due to the irregular shapes of output areas. But overall I believe it's the case that the numbers reflect pretty close to the true population so I think, based on my initial 1km grid, that the area in Bow (East London) is the most densely populated 1km square in the UK, with a total of approximately 21,000 people in the 1000 x 1000 metre square. 

Ah, but hold on now. What were we saying about moving the grid around and the impact it might have? Well, I also generated three extra grids and ran the calculations on those, so read on for my final answer!

The answer to the question is finally here

With my first alternative 1km grid I once again got figures of just over 21,000 in any given square km, but I got seven of these. With my next one I got three squares, two of which had more than 22,000 people in them. With my third I got three as well,, one of which had more than 24,000 people in it, and one of which had 23,000. See below for maps of these. The three top squares from my original grid are shown in red on these maps, for comparison.

Shuffle the grid, get more answers, but similar areas

Three alternative candidates

I think we have a winner

So, my initial grid seems to have not been very far off the mark in helping find the most densely populated square km in the UK. Yes, we could go on and on with grid placement, and do it programmatically but I think we're always going to end up in the same place, around Bow Common in East London. It's also encouraging that the 20,000 to 25,000 per sq km figures I previously calculated come out here too. By way of comparison, the most densely populated areas of Paris or London (or New York or Seoul) have more than 40,000 people in them, and some over 50,000.

The overlap here is the initial winning candidate from my search

So, based on all of the above, my answer to the question of where the UK's most densely populated square km is, is Bow in East London with a population of approximately 24,000 in a single square kilometre, as shown below. Yes, there is a bit of fuzziness in these numbers due to not being able to perfectly align grid squares to output areas but I'm fairly happy with the answer I arrived at here.

I think this is a plausible answer to the question I posed

Hey, hold on a sec! What, not more density numberwang? Yes indeed.

I'm happy with my answer, but just to prove beyond any reasonable doubt that in these kinds of things the answers you get depend upon your method I decided to cheat a little and see if I could use a random 1km grid approach to find any area with more than the population in the square above. This is not really in the spirit of the method because it's not applying a regular grid across England and Wales so I don't consider this the 'proper' answer. Instead, consider it an approach to find an even higher value, for research purposes. The location of the 'most densely populated square km' in the United Kingdom doesn't really change and that's the main thing. 

Here's what my 1km 'grid' looked line when I was on the hunt to find a higher figure than the square above. This is almost 28,000 separate 1km squares but they do not form a grid, so I consider this method a bit of a cheat so I don't use it as my final answer above, but I wanted to see what happened when you did it.

Lots of squares, but not a grid approach

Then we can filter for areas with above 24,000 people and see what we get. That's what's shown below, and the square from the answer above is highlighted in red here for comparison.

Ruh-Roh, spanner in the works? 

Is this now a showdown between West and East London for the title of 'most densely populated square km in the UK'? Well, maybe, but only if you're using this cheat method of single squares. So who wins on this approach? See below for the zoomed in maps with the numbers.

All over 24,000 here (remember this is approximate)

East London wins again (original winner in red)

So, as we can see, the answer to the 'where is the most densely populated square kilometre in the UK?' question doesn't seem to change, even if we cheat and allow ourselves to place our 1km squares randomly in order to maximise the single square total. The area in the map above has four new squares with 25,000 or more - though of course these numbers are an approximation of course, as I've explained above. This kind of cheating approach does however have the benefit of showing how areas of West London come close to being the highest density if we play a bit of gridshift.

What does this actually look like on the ground though?

Here's a Google Maps link to more or less the centre of the red square above, which is also pretty much in the middle of the blue squares. Here are some images from Street View - and recall that this is what about 25,000 people per sq km density looks like in London. This is half the density of the highest density places in Paris, Barcelona or New York, and about a quarter of the highest densities globally (found in cities like Manila, Cairo and Dhaka).

Burgess Street, E14

Broomfield Street, E14

Lindfield Street, E14 (still space for parks)

Are we done now?

Yes (for now).

Arterial Cities

I was recently experimenting with some circular city layouts in QGIS in preparation for my Automatic Knowledge QGIS training sessions. After a bit of playing around, I ended up creating a set of city models in Aerialod. I'm calling them 'arterial cities' because they show cities criss-crossed by major arterial road and rail routes but also because they're kind of art as well. I've now done this for 50 towns and cities across Great Britain - using a 5 mile diameter circle on top of a 10x10km plinth. Here's a close-up of one of the London ones (below). I've posted a selection of the others further down, but if you want the original high resolution images for 50 towns and cities you can find them all in this folder. As one of my earlier tweets said, this might be a useful way to show how cities are divided by road and rail infrastructure and highlight things like urban permeability. If you want to learn about the method, scroll to the bottom of the page.

London in a new light

Some examples

The final set of 50 arterial city models include the major cities plus a selection of other places, chosen for a variety of reasons such as location, urban form, size, and a bit of personal preference. For London, Cardiff, Birmingham, Leeds, Manchester, Glasgow and Edinburgh I also created some large, re-coloured, and also zoomed-in renders and you can find them in the shared folder as well. Ok, so let's take a look at some of them, starting with Leeds, because it's really quite fascinating. I'll say a bit more about specifics below, but in all the graphics the rail lines are the highest features, followed by major roads and then minor roads, with buildings being slightly higher than the minor roads. This 'major' / 'minor' thing isn't perfect of course but that can always be tweaked.

Lots of big roads and rail lines (I've recoloured this one)

Glasgow has lots of roads and rails

Spot those motorways

Quite a pleasing ring road here

A real cross-cross of routes

No hills are shown in any of these

Lots of barriers

A very interesting one I think

Interesting compartments here

A real mix of old and new patterns

Hopefully there is something here that you find interesting. Let me also post a few of the zoomed in versions I did, focusing on the lettering in the top left of the plinths. I've changed the sun direction on these ones so it's coming from the north.

Little details that I find interesting

I've done quite a lot of visualisation with Aerialod before and written up a few tutorials but this is the first time I've made this kind of graphic and it wasn't planned. Even so I think the approach can be quite useful at highlighting city structures and there are a number of elements in the design that interest me. The first is when the text of the city name overlaps the city fabric, like in the Newcastle & Gateshead example below.

I just like the way it looks

I also like the way the railway lines in some cities appear to fray at the end, as the lines diverge to different platforms - like in the example below showing Euston, St Pancras and King's Cross in London. 

I just like the way these look

Then of course we have other features like roundabouts and grid patterns, for which we can use Milton Keynes as the pre-eminent example. I think the light and shadow does a good job here.

There are more roundabouts than you can see

In quite a few of the coastal cities it looks like there is only half a city, just because when I extracted the images from QGIS I did so using a distance of 2.5 miles from the city centres. So for places like Hull, Brighton and Bournemouth you'll see half a circle. But in other places it shows how they are connected to places across the water, as in Liverpool or in Dundee (below) and I quite like this tethering effect.

Tethered across the Tay

Also quite interesting, given that Euro 2020 is now in progress, is the way you can see many football stadiums and this can often help us get our bearings when we see them. So, for example, in the snapshot below we can see Celtic Park to the east of the image and Hampden to the south of it. This one below has also been recoloured, like the Leeds example above, but they are both available in the original gold tones in the shared folder.

Hampden: home of the Euro 2020 champions

There are loads more interesting details, so I'll leave you to look for yourself. For now, I'll leave you with Oxford because I think the urban structure here is both unusual and fascinating. 

Take a look at the real place on Google maps

Okay, so that's the graphics and what I think about some of the details. The rest of the post is about how I made these so read on if you want more information on that.

If you want to make your own prints out of any of the graphics on the shared folder, be my guest.

Stage 1: prepare your images in QGIS

For these graphics I used OS Open Zoomstack data and specifically the five layers below - they are layered in this order in the QGIS Layers Panel and the greyscale colour I used for each of them is shown in brackets. The greyscale colour values determine how much or how little Aerialod extrudes features because that's just how it works - white (#ffffff) will be the highest and black (#000000) shows up as a hole, just like the little Ordnance Survey credit in the bottom left of my images above. I quite like using black to give a kind of cut-out effect with text.

• roads_national (0.35 line thickness, #4d4d4d - this is 30% greyscale)
• rail (0.25, #595959 - this is 35%)
• roads_regional (0.25, #404040 - 25%)
• roads_local (0.1, #262626 - 15%)
• local_buildings (#2b2b2b - 17% and with a 0.05 mm stroke width on the building polygons)

I prepared these in the QGIS Print Layout using the Atlas tool so I could automate it (see my previous tutorial on that) and I added text labels for the city, my twitter handle (bottom left) and the OS credit (bottom right). The background page colour in the Print Layout is #1f1f1f (12% greyscale) rather than black because if it's black it won't show up in Aerialod - although this is good if you want to make these without a square plinth. 

What they look like before adding them to Aerialod

Then I just exported the images at 1200dpi as png files straight out of the QGIS Print Layout. I have put all the images in this shared folder for anyone who wants to try making the graphics in Aerialod but doesn't want to do the QGIS bit.

Grab the raw images here.

Step 2: load the images into Aerialod and go wild with the settings

Aerialod is an interactive path tracing renderer for height maps in Windows and that's what I used to create the graphics on this page. It is pretty easy to get started but it can also be a bit baffling and there are so many options - many of which may not be obvious to the casual user. So, rather than mess about telling you what I did and making all kinds of suggestions I'll just show you the settings I used to create these images, in the screenshot below.

I exported these at 3840x2160 pixels

The only thing you need to be aware of is that it could take hours to render just a single image at this size - it all depends upon your computer. I have quite a powerful machine with 64GB of RAM, an i7-10700KF CPU running at 3.80GHz and a NVIDIA GeForce RTX3070 graphics card. Without the latter piece of equipment in your machine - if you just have a basic graphics card - the rendering could take hours, or maybe never.

You can spend hours, days, months messing about with the settings in Aerialod and there are an almost infinite range of possibilities in terms of light, shade, colour, tone, extrusion and so on. You can of course achieve similar things using tools like Rayshader or Blender but Aerialod is deceptively simple, yet impressively powerful in my opinion (once you get past the initial steps of what does what).

One thing that is not immediately obvious, or indeed obvious at all, is how to achieve the blurred/focal point tilt-shift effect you see in the example below for London. This is done by clicking on the area of the map you want to be in focus. When you do that, the Focus setting on the right of Aerialod changes and you see the blur effect everywhere you didn't click.

You can go round in circles with this kind of thing

Note the Focus value on the right

Want to achieve a totally different, less glowy kind of aesthetic? Well here are some other settings you might like.

The key difference here is the 'SKY' setting on the left

And one more, like above but slightly tweaked.

Intensity (left) and Exposure (right) adjusted in this one

And if you want to remove the plinth completely, you just need to reduce the Offset value on the right in Aerialod, as shown below.

I also quite like the plinth-less approach

This is the big plinth-less version, rendered as above

This is my way of doing it although if you see the original twitter thread mentioned above you'll see loads of different kinds of examples. 

Hey, could you do it with buildings extruded more realistically in 3D? Yes, but that's for another day.

In this example I've used building height data from Emu Analytics