and those who live in London doesn't allow enough houses to be build to lower the cost?
Everyone should remember that 60 years ago London housing was very poor as well as relatively expensive (although far more attainable). That's important as it shows that things can and will change over time in the market. We need to think about this because some of the reforms suggested will fundamentally alter the physical geography of the city in ways that will have consequences 100's of years into the future. Architects and planners have a very bad track record with respect to these alterations, for example see Birmingham, Portsmouth, Ipswich, Reading in contrast to Manchester, Brighton and Bristol where history has run differently (Bath is a really good story - the 60's got stopped in its tracks there).