a) There are ~850k housing benefit claimants in Greater London[1], out of a total population of just under 5mm.[2] That's ~17%. Not a majority, to be sure, but also not small enough to discount entirely.
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...
