The latest instalment of our weekly series, in which we use the Centre for Cities’ data tools to crunch some of the numbers on Britain’s cities.

“Why,” my few remaining friends often ask me, after I have cleared another party by boring on about housing policy once again, “are you so obsessed with the green belt?” And the answer is that I sometimes don’t really enjoy parties very much, and this is less effort than taking control of the music and playing Living on a Prayer until everybody else runs for their lives.

But the other reason, of course, is that – at least, in its current form – the green belt imposes terrible distortions on Britain’s housing market. It means we can’t build in those places where demand is highest (London and the south east, Oxford, etc.). But we can build in places that are much further afield. Development effectively jumps the green belt to those towns just outside it (Milton Keynes, Swindon, Bicester etc.). The result is longer commutes, bigger carbon footprints, and so on.

All this is a bit assertion-y, though, so let’s look at some data. This map show the percentage increase in the housing stock between 2009 and 2014 in the largest British cities.

The thing that leaps out at you, I think, is that nothing leaps out at you. Demand for housing is highest in the south east – but while some towns and cities there do tend to have built more homes, plenty of others haven’t (Brighton, Aldershot, Luton, Southend).

Meanwhile, while the cities that have built fewer homes tend to be more affordable northern ones, there are others that have grown rather a lot. Warrington (3.2 per cent increase in housing stock) is a bit of a boom town; Barnsley (3.7 per cent increase in housing stock) isn’t.

Scotland, as ever, insists on mucking up this nice neat pattern, so thanks Scotland.

So – while there’s little sign that we’re building more in cities where demand for homes is highest, there’s little sign that we’re not either. What we really need is more data.

This time I’ve plotted the increase in housing stock, 2009-2014, against the mean house price in 2009. House prices are a proxy for demand for housing – so, in a fully functioning market, of the sort economists comfort themselves with, you’d expect higher prices to translate to more house building.

And yet:

At the very top of the chart you’ll find Milton Keynes, which is chucking bricks up all over the place despite relatively affordable housing. Cambridge is expensive and growing; London more expensive, and growing less.

Worst of all, as so often when looking at housing, is the situation in Oxford, where house prices are terrifying – yet almost nothing gets built.

The correlation co-efficient of those numbers is 0.24. In other words, there is barely any relationship between high house prices in 2009, and an increase in a city’s housing stock over the next five years.

One last chart, this time plotting increase in housing stock against the increase in house prices. This one’s a flat image, for page load time reasons, but we’ve labelled the outer ring of cities. They might be a bit familiar.

This time the correlation co-efficient is 0.35 – stronger, but still, by most statistical standards, weak.

These figures don’t prove that the green belt is at the root of all our problems. I stand by my belief it does, because Oxford and Brighton are among the most tightly physically constrained cities in Britain – but I can’t actually prove it.

But these figures do give a pretty strong indication that trusting to the market isn’t going to solve the housing crisis. Prices get higher – and yet still, no one builds. If we’re ever going to fix this mess, the government will have to take action.

Jonn Elledge edits CityMetric and tweets too much.

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