Great news, Londoners: the capital doesn’t have Britain’s biggest housing crisis. Let’s hear it for Oxford where, relative to wages, prices are even worse. Yay, Oxford, woo.

This thrilling news comes from a report from the Centre for Cities think tank, published today, on the never less than entertaining train wreck that is British housing policy. The report as a whole is kind of a good news/bad news thing.

Take the bad news first. In the most over-heated cities – which also include Cambridge, Brighton and Bristol – high housing costs are a side effect of economic success. These places have lots of jobs, so attract lots of new residents, but because they’re not building enough homes to house all these people, prices are inevitably going up.

This doesn’t just hurt those paying through the nose for a roof over their heads, the report argues: “This matters to the national economy as well, because these cities are the most productive”. So, high house prices are hurting us.

There’s more. Recent housing policy has focused on building more on “brownfield” areas – land that’s been developed at some point in the past – as a way of preventing urban sprawl. However you look at it, though, there isn’t enough of this to meet demand. Oxford has enough brownfield land for less than 2,000 homes; it needs an estimated 30,000. London needs something like 50,000 extra homes ever year; it’s not building anything like that, but if it was, it’d run out of brownfield land within a decade.

That’s the bad news. But! It turns out that actually, we have loads of space for housing. To build 1.4m extra homes, at low-density, and near existing infrastructure like railway stations, we’d only have to build on 5.2 per cent of the green belt. If we built on 12.5 per cent of it, we could have 3.4m homes. All our problems would be solved, and we’d still have 90 per cent of the green belt the go for walks in.

Then it’s back to the bad news, which is that nobody with the power to make this happen wants to because the pro-green belt/anti-building lobby is basically all-powerful.

So, that’s all good.

The key message of the report, though – the one overriding lesson it contains – is that Britain needs to free up more land for building. That’s basically non-negotiable. So, if any of Britain’s politicians do fancy growing a spine, the Centre for Cities has a few recommendations as to how we can do that.

1. The catch-all “green belt” label isn’t massively helpful: we need to “evaluate land on its merits rather than its existing designation”.

In other words, we need a more nuanced planning system that can distinguish between, say, scrubby wasteland which would be perfect for development, and genuinely beautiful countryside.

2. “Brownfield” land often requires state action to make it appropriate to housing. That means infrastructure, land assembly, even direct development. That’ll all cost money, and political will.

3. The economic footprint of cities often extends across local authority borders, whether to contiguous built up areas or commuter towns miles away. Councils should thus be incentivised to work with their neighbours when working on housing plans.

The report contains other, more technical suggestions, too: streamlining Compulsory Purchase Orders, to make it easier for councils to assemble land; allowing cities to buy land at its current value, so that they, rather than previous owners, benefit from the increase that comes with planning permission; create development partnerships between councils and builders, which will be able to borrow to invest.

All this means that there’s no quick fix. If we’re ever going to solve this mess, we need use brownfield land and build at higher densities and re-designate parts of the green belt.

But – we can solve it.

Here, for your delectation, is one last map. Build on just a fraction of the areas marked in red, which are all within 2km of railway station, and we could solve London’s housing crisis. The full report is available here.