The law doesn't say you can't build parking spaces with the dwelling(s) nor does it make it harder to include parking in the proposal for the dwelling(s).

How much is housing in Soho, Central London, and Tokyo again?

Must be cheap based on this metric. Remember that soho has one pretty crappy subway station, so it’s not particularly transit rich.

People will buy there because it is slightly cheaper. And then it will all fail, because the limited parking will be filled with cars and everyone will complain.