If you're trying to imply the housing shortage only exists because rich people have too much money and are making prices too high for everyone else, that doesn't make much sense. If everyone had the same amount of wealth, you'd still have the same housing crisis. Specifically, there's still going to be the same amount of houses in London, and the same amount of people who want to live there but can't. The problem of housing in London is that there isn't enough for everyone who wants to live there, not that the rich are making prices unaffordable.
And why might that be? Could it be that the rich are using their wealth and disproportional influence that wealth gives them to slow down or block new development to keep their property values high, or are we supposed to believe that places where housing is used as an investment vehicle are just naturally incompetent at building more housing?