> "You would probably have to demolish large areas of London and replace them with high-density housing to match demand - but obviously that's never going to happen."

Nah. There's still many areas of fairly low-quality, low-density housing near the centre of London. In fact, just about everywhere you look there are residential towers under construction: there must be hundreds of them going up right now! There is still plenty of scope to greatly improve the quality and efficiency of housing in London without sacrificing open, green spaces.