I just have a couple of things to add.
As the Campaign to Protect Rural England points out repeatedly (and will do at greater length when they release their report at the end of the week), this is no simple supply and demand situation, where prices go up because there isn't the space to accommodate the people. Overcrowding in houses has gone down and, commensurately, the space per person has gone up, nationwide. The only important problem is that property has become an investment, and as a result prices have shot up way beyond what simple market forces would dictate.
The Campaign to Protect Rural England are a single-issue lobby, and their single issue is "Don't build any new houses outside of towns, ever." They oppose new houses being built in the middle of fields, they oppose new houses being built in small villages, and they oppose new houses being built on the outskirts of towns, as that would make the towns bigger. What I'm saying here is that their report might be a tad biased. I'm not saying it should be discounted entirely, but it might not be a great idea to base one's entire argument on it without considering some other sources of information.
The Campaign to Protect Rural England and their ilk have been very successful. If you own a bit of land in the countryside, you're allowed to put cows on it or have a picnic on it, but our councils' planning departments aren't about to let you build on it, no matter how ugly it may be. The powers that be are simply refusing to let our towns get any bigger.
Supply and demand are far simpler than Zoe Williams seems to realise. There's loads of spare land in Britain, but the supply of land that you can actually build on i.e. land in towns and cities is driven artificially low by planning regulations and driven even lower by the fact that most of it has already been built on. Meanwhile, more and more people are choosing to live alone ("Overcrowding in houses has gone down"), driving up demand for residences. So, since there's nowhere to build new houses, those new residences are created by developers who buy up houses in towns and turn them into blocks of flats.
Scrap the planning regulations, and houses will become affordable again.
All of which is fascinating, but my real question is this. Since when do Guardian writers complain about how some people can't afford to buy their own houses? I thought Socialists were all for renting especially renting from the state. After all, owning a house is Capitalism, isn't it? When Thatcher gave council house tenants the right to buy their properties, Socialists were up in arms about it: it would hurt the poor, they said; the poor needed to be able to rent affordable housing, they said; the poor don't need to buy their own houses, they said; you must build more council houses, they said. Now here they are, complaining that some poor people are having to rent their property because they can't afford to buy, and criticising the government's plans to deal with this by building more council houses. Is Zoe Williams going to publish a piece called "Thatcher was right", I wonder?