The Labour run authority says it is looking forward to working with Andy Burnham but he must address several issues in the borough.
Right to Buy was introduced in 1980 under Margaret Thatcher.
The aim was to give the most secure council tenants the legal right to purchase their homes at substantial discounts.
Ms Thatcher was vocal about creating a “property-owning democracy” to break “dependency on the state.”
But Lambeth Council wants the practice banned.
Instead, it says low-interest loans should be made available to councils, enabling them to build more council homes.
Lambeth also wants to be allowed to keep the proceeds of the proposed Mansion Tax and the Overnight Levy.
