In the news

Well. The world's cities are under unprecedented inflow pressure, largely owing to increasingly rampant internationalised injustice. People are fleeing smaller places (countryside, villages, towns, and cities) in droves, partly because they are pulled (attractiveness of economic opportunities in cities), partly because they're pushed (lack of attractive economic opportunities away from cities). Housing is only a symptom of that; you can play around with the housing market to your heart's content, but it won't solve the underlying problem.

I take it your question is whether similar policies on housing could happen in London? I think the chances are very slim, certainly under the current government, but there is the Brexit uncertainty factor. Then there's the office of the Mayor of London, relatively powerless compared to city mayors around the world, and I imagine the government would want to keep it like that for now.

At present, London's planning policies are pretty poor and in a sense the horse has already bolted. There is still a hope that at least some of the rubbish high-rise development in Central London can be halted, but as Mayor of London, Sadiq Khan is in a double bind. On the one hand, it's his job to benefit the city he governs, which in the simplest terms means 'growth'. On the other, he's Labour and probably does understand that growth in just the one place doesn't help the country at large a great deal. I don't know whether Khan will manage to leverage any more powers for himself. If he does, I consider it unlikely that he would be given adequate power to address the underlying problems apart from tinkering with housing a bit, i.e. set a certain price level for 'affordable' housing that would probably still be unaffordable to the vast majority.

Not much of an answer, but I think things have to change much more politically before housing policy stops being as unjust as it is at present.