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 don't really think this has much significant impact on the housing shortage and pricing there, but some part of the housing stock there is owned by people who don't actually live there, and who can afford to keep it vacant just in case they need to move in one day.