You can already build in the city. In fact, New Labour put in subsidies and incentives to build multi-storey houses, which are probably still in place. So why don't developers just go and replace low-rise with high-rise? Because nobody really wants to live in flats in England if they can avoid it. It's a cultural thing and it has nothing to do with land scarcity, it's probably a result of the failed '70s projects mixed with the hardcore individualism that emerged since then. This drives down prices of flats to the point where it's not appealing for developers to build new ones (except in the immediate vicinity of SW1 or other areas that are attractive to singles and childless couples, who can be persuaded to fit into tin boxes). What sells is low-rise suburban, for which they are running out of space; hence the push for greenfield liberalisation. Everything else is divide-et-impera rhetoric, boomers vs impoverished etc etc.