The idea that housing benefit is driving the rental market is total nonsense. a) it forms a minority of the market and b) the majority of landlords won't let to people on housing benefit.
b) Just because some landlords do not want to deal with non-claimant tenants doesn't mean that non-claimant tenants will only want to rent from such landlords, if it means cutting themselves off from lower rents. Theoretically removing those 850k people from the housing market would undoubtedly make the prices fall, if only for a while.
1: http://www.londonspovertyprofile.org.uk/indicators/topics/re...
2: http://en.wikipedia.org/wiki/Demographics_of_London#Populati...