Anyway, my answer would be much of east London between the City and Canary Wharf
(Shadwell, Stepney, Limehouse).
One problem is that transit isn't great (the DLR is there, but capacity doesn't match heavy rail). But it's located between two of London's main office/skyscraper districts, and the building stock is largely 1950s/60s council estates (the area was heavily bombed in the Blitz) which could be redeveloped en masse without losing historical structures.
The other area is right across the river in
Rotherhithe and the old
Surrey Docks. This is another area that lacks historical neighborhoods, but was redeveloped in the 1980s when London didn't have the housing demand that it has now. The transit is good (Jubilee line and overground), and proximity to Canary Wharf, Southwark and the City should make it a prime residential and entertainment area. Instead, its full of underscaled housing developments on cul-de-sacs (like subdivisions) and an actual shopping mall with surface parking.
This is an old map showing both sides of the river. The City and Southwark are to the left, the Isle of Dogs on the right is now Canary Wharf and other housing. In between is a poorly planned area developed between the 1950s (north of river) and 1980s (south of river), which is all totally out of place given its central location:
Both of these areas should be torn down and rebuilt from scratch if one wants to address London's housing shortage. It would have to be done in phases, but at massive scale, because the roads would need to be rearranged as well.