Chris - People not in receipt of any benefits are effected by external market prices, those in receipt of benefit shouldn't be immune to them. Prices outside of London may increase, but considering the pirce differences it would take some time for them to hike up to London levels. Not everyone can live in the South East, whether they want to or not.
I have no issue with social rent houisng being built, although forcing private rental caps is a whole different kettle of fish. Unless there are a ton of people waiting to be housed in london who can afford those private rents, the rents will surely drop when private landlords can no longer fleece the public purse for the money. As for your universal benefits comment, I'm failing to see how benefits have been so bad up to date, the benefit system was long due for an overhaul, and I'm sure when UC comes in and tenants start pocketting the cash it'll be the landlords that'll be suffering.