Wandsworth Council has secured eight properties in and around Birmingham and is offering its council tenants 'bribes' of up to £7,000 each to move into them.
It is the latest London borough to adopt the policy of relocating tenants to cheaper homes in the Midlands and North to free up high-demand housing in the capital.
The policy has been slammed as "social cleansing" with critics claiming it is a back door attempt to gentrify areas of London by moving out low income families.
But others say the incentives are being used to encourage pensioners to free up larger homes for families.
Wandsworth Council, which includes the up-and-coming Battersea area, said it had deals with private landlords offering eight properties in the Birmingham area and so far three had agreed to move.
A letter to tenants, circulated by a Wandsworth Labour councillor Simon Hogg, said the properties in Birmingham were less expensive to rent and often came with a garden and driveway.
Households are offered £3,500 to give up a two-bedroom house or flat, rising to £5,000 for a five-bed property. They are also offered up to £2,000 to help with moving costs.
Coun Hogg tweeted: "Unbelievable letter to council tenants from Wandsworth Tories: 'We'll pay you to move to Birmingham and rent privately'."
Birmingham City Council's Labour leader Sir Albert Bore has previously written to London boroughs urging them not to dump their homeless families on Birmingham without informing the council because many are vulnerable or need social service support.
He said: "This is the first example I've seen of a letter along these lines to tenants but we have been aware of certain London boroughs seeking to obtain private rented sector property in the city.
"Officers have been making real efforts to engage with their counterparts in London on this issue and we have discussed the matter at a political level.
"Despite these efforts, and the fact London boroughs should notify us when individuals are moved to Birmingham, the reality is they have not done this consistently.
"Officers in our homeless service will speak to their counterparts in Wandsworth for a fresh update on the current citywide position.
"However, the bottom line is we are left dealing with the consequences of an appalling and short-sighted government policy that shifts vulnerable people out of London and puts more pressure on housing supply in Birmingham."
He was also worried about the impact on Birmingham's own housing and homelessness problems.
A spokesman for Wandsworth Council said: "This is a scheme that has been in place in Wandsworth for many years. Every other London borough has a similar policy.
"What it does is provide choices and incentives for tenants in larger properties to hand them back so they can be used to provide new social rented homes for families on waiting lists who may be living in overcrowded conditions and need a bigger property.
"Offering a financial incentive is one of the ways in which tenants who don't need such big homes can be encouraged to give them up.
"As the letter makes crystal clear, it is not compulsory and no-one is forced to leave but some residents are quite happy to move out of London because they may have family connections in other parts of the country or are looking to make a fresh start outside the capital."