This is demonstrably not true in London where rent
    just keeps on going up and hardly any new housing
    is being built.

http://www.london.gov.uk/priorities/housing-land/renting-hom... claims only a quarter of people in london rent? So the "if everyone rented" bit isn't being met. Because property values and rents mostly move together, as long as most people own their homes you have more people backing policies that push them higher than lower.

I don't know the London political situation very well: what makes it so expensive to build new units? Are there strict historical preservation laws? Rules that let neighbors veto or slow nearby construction? Permits and taxes?

    He can't afford to rent a 4 bedroom house
    anywhere near Westminster

"Anywhere near Westminster" apparently means "within walking distance". A 30min public transit commute covers areas where renting a 4br would be ~£26/year.

    you can expect it to be under water for a few years

I'm not sure what you mean by this. You're saying if you build a flat and sell it then people are buying them at prices at which they wouldn't be able to resell them? Is this just because there's a premium for new construction? (Cars in the US, for example, lose ~20% of their value when they're bought for the first time because they stop being "new". So you could say that if you buy a new car you expect to be "under water" at first, but no one would say that.)