Deputy Leader is a bit of a side show right now - Labour will be judged on housing, crime and the cost of living at the next election. Whoever hold those briefs determine the outcome of the next election.
Before you jump on me - it's perfectly possible to install high quality modular social housing in 4 months. What we lack is the political will to get it done. We need speed, ambition and an explicit commitment not to sell the lot off again (use of co-operative trusts would work here). Or - since everyone is hungering for the 1960s, why not give councils the power to build again? Why so we have to rely on private housebuilding?
I would also look at the private housing market, especially where investment portfolios are buying up properties and leaving them empty.
Edited for typos