A lot of London building stock is protected, and should be. Otherwise it's actually quite friendly to developers from the looks of things. There are restrictions on tall buildings in certain areas and along certain view corridors, but one look at the scattered high density development all over Greater London will show that it's not that hard to build big buildings.
The problem here is building new affordable housing, although a lot of existing stock in central areas is owned by councils, which further drives up the price of market apartments. Labour wants to allow building on greenbelt land which is, in general, a bad idea. What's needed is higher density, affordable development on brownfield or otherwise underdeveloped (but not worth preserving) neighborhoods.
A great example of this is the Surrey Quays area between Southwark and Canary Wharf. Former docklands developed in the 1970s and 80s when the land wasn't so valuable, so it's very suburban (there's even a mall), but it's right in between London's two main financial districts and on the Jubilee line. The whole peninsula should be torn down and rebuilt from scratch, but there's local opposition even to redeveloping the shopping center!
It looks like this today:
https://goo.gl/maps/QfKFrWMTa9t