I don't think there's anyone in any western government that wants to reduce rents or housing prices. They all have property portfolios.
I'd be more interested in redistributing land in the UK, away from the governments and charities, and into the hands of the general population, and revoking planning permission laws. After all, they're building big ugly solar and wind farms everywhere, so why not housing?
Forestry Commission, National trust, RSPB, Crown Estates, CofE, etc.
All need disbanding and redistributing to the people.