Spend any time mired in the depths of Britain’s housing debate, as I do, and you’ll notice certain solutions popping up again and again. Some blame the crisis on planning policy, and so think we should rethink the green belt; others prefer to blame it on foreigners, and so think we should leave the European Union. Each to their own.

One of the supposed solutions that tends to pop up quite a lot is as massive increase in the scale of Britain’s social housing sector. Once upon a time, the thinking goes, Britain built a load of council houses, and it didn’t have a housing crisis. Then we stopped building council housing, sold off large chunks of what we had on the cheap, and now we do. QED.

Whether turning this particular clock back can get us out of this mess is an open question. But it’s worth noting that there isn’t really any correlation between the house prices in a British city, and the prevalence of social housing within it.

First things first – where is social housing still a thing? This chart shows the percentage of households living in social housing in 62 British cities at the time of the last census. We sorted the data from highest to lowest percentage, then colour-coded the bars by region.

Two conclusions present themselves from this. One is that the numbers are all over the map. The city with the highest proportion of households in social housing (Dundee, with 30.1 per cent) has more than times as many such households as that with the lowest (Southend, with 9.1 per cent). That’s a big range.

Secondly, there isn’t much of a regional effect. All too often these posts descend into a meditation on yet another aspect of the north-south divide we’ve just discovered, but that doesn’t seem to be the case here. Scottish cities do seem more likely to have large populations in social housing, and southwestern cities less likely; but those in most other regions are scattered across the chart.

The next question is – what does a large quantity of social housing do to house prices?

Not, it turns out, a lot.

That’s a correlation of -0.21. It means that an increase in social housing is very slightly correlated with a decrease in housing affordability (a ratio of house prices to incomes). But it is very slight – it’s not a statistically significant correlation.

This, if you think about it for a moment, makes some sense. You’d probably expect economically depressed cities to have a substantial portion of council housing, simply because the Thatcher home ownership revolution and right to buy never took off.

But rich cities often need subsidised housing, too, simply to counteract the fact that, otherwise, vital workers can’t afford to live in them. Around 80 per cent of Singaporeans live in public housing – in one of the richest cities in the world. The relationship between house prices and social housing is a complex one.

All of which is a lot of words to demonstrate the mildly obvious fact we should probably have never expected any relationship between social housing stats and house prices in the first place.

That said, building a new generation of social housing probably would help with the housing crisis – but mostly, one suspects, because it’s building a load of housing. The reason the era of council housing coincided with relatively affordable house prices may have been less because the state owned a lot of housing, but because it built them in the first place.