Social cleansing will occur; only its extent is uncertain.
In the private sector, there will be cases where the diminishing ability of tenants to pay (unemployment, cuts in housing benefit) will cause the landowners to decrease rent; this will be particularly so in bedsit-land and in the junk estates. Alternative tenants with more money simply don’t exist.
In those areas, especially London, where there are potential tenants who can afford the existing rent levels, only philanthropic landlords will reject the route of attempting to dump their existing tenants and seek out higher paying ones.
Forcing people out of their homes is one of the most traumatic things that can happen to a person. Expect incidents of family breakdown and suicide to increase.