The sum could be docked from the authority's rebate, paid by the Department for Social Security, as it has failed to ensure all claimants are bona fide.
A council spokesman said Lambeth was making plans to cope with potential losses of£3m but added: 'That's not to say it [the council] is liable. It's not to say the losses are there.'
But he also said that it was likely an extra£500,000 would have to be spent on more management support for the housing benefit contractor Capita, via a joint management board.
Tom Franklin, the council's leader, said: 'The figures are still a long way from being acceptable, and improvements, although substantial, are proving to be challenging to maintain as we work our way through the hardcore of backlog cases. However, the council will not rest until we have the situation firmly under control.'
He also expressed concern about the complexity of administering housing benefit, which he says smothers councils in rep tape. In the past two years, Lambeth says it has had 169 circulars from the DSS on housing benefit alone.