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.
Most buyers of such property (whether private or investment funds like Deka-Immobilien or BlackRock Global Property or Brookfield Property Partner or one of the many others) do this as an investment vehicle with a particular risk/reward structure. They will absolutely have to rent out these properties, and indeed, when they fund property construction projects, as they have been on a massive scale in London in the last decade, they do so to cash in on rent.
I would imagine that a much bigger issue is old people who are in a care home or a hospital, unable to live in their old place, but not willing/able to give it away either.
At least over here (Finland) this is the major reason for "empty" apartments in central areas of cities.