1. Remove density and height restrictions (e.g. "Berliner Traufhoehe").
2. Remove unnecessarily strict building requirements (e.g. "Daemmungswahn").
3. Remove legislation that is too tenant-friendly (e.g. "Mietbremse").
All three serve as breaks to increasing housing supply, the first is a legal impediment, the other two reduce investments.
Doesn't really help getting more affordable flats on the market.
I'm not sure how familiar with the London property market. London is currently seeing a large amount of real estate being built, mostly studio, 1, 2 and 3 bedroom. Hardly luxurious. Prices are commensurate with London income levels. Otherwise people wouldn't live in London.
I feel like most people are moving to the outer zones. Buying flats in zone 1-3 is obviously out of reach for most people, even for most developers not working in The City. From what I've seen, even 1-bedroom flats cost at least £310k near Seven Sisters (Zone 3).
I have to admit though that I was mostly looking for flats to rent, not for sale in the last few months so I'm not an expert.