The new leader of Wandsworth Council has said he will lead a "radical reform" of housing in the borough.
Councillor Ravi Govindia wants to give greater priority to people on the housing register who are working.
The Conservative-led authority said the move would encourage households to be economically active rather than to "race to the bottom".
Charity Shelter said Wandsworth needed to increase the amount of housing rather than "fiddle" with allocations.
A council spokesman said residents currently qualified for housing on the basis of vulnerability instead of progressive grounds, and quoted the Mayor of Newham, Sir Robin Wales who reportedly called the result of the policy "a race to the bottom".
The spokesman stressed that homeless people would still qualify for social housing under the plans.
Roger Harding of Shelter said: "If you are judged to be homeless, the local authority has to provide you with a secure place of accommodation, and I think that is absolutely right.
"We have a very limited number of social housing in London at the moment and we can fiddle around with the allocations - as Wandsworth want to do - about exactly who gets it but a good many of us are still not going to be able to access secure affordable housing.
"What is going to change that, fundamentally, is us building a lot more of it [social housing] and that's going to need councils like Wandsworth building a lot more of it than they do."
The new council leader said he was also looking into the possibility of introducing a deposit scheme for first-time buyers, funded from housing receipts and future development, which would be paid back when the property is sold.
He said: "Just as Right to Buy has helped millions of people since the 80s, we need to look at new ways of helping a new generation of young people into home ownership.
"Ideas such as a new deposit scheme would help end what is fast becoming a generational divide between those who can afford a stake in their property and those that cannot."