Under the terms of the mayor's London Plan, half of all new homes in the capital should be affordable and 70 per cent of these should be available at affordable rents.
"It is disgraceful that Wandsworth councillors should ignore their poorest residents by failing to make any provision for them," Livingstone said.
"If we are to tackle London's housing crisis, every borough must play its part and plan ahead to build the right amount of affordable homes, which are needed both by their own residents and Londoners as a whole."
He said Wandsworth's strategy is contrary to the London Plan, adding that it is likely to be rejected by the Planning Inspectorate.
But the council complained that the mayor's focus on a target of 70 per cent affordable homes for the rented sector will mean that less housing is available for first-time buyers.
"The mayor has jumped the gun to make a lot of noise about housing targets. He seems not to be allowing councils to have the right to make their own policies," said a council spokesman.
He admitted that the plans in the borough's local development framework called for a "broadly even mix" of affordable rented property and affordable housing for sale. However, he said a final decision would be taken after the results of its housing needs study.