The council is going to house homeless people outside the borough because it is too expensive to house them in Wandsworth.
In a move, highlighting Wandsworth’s housing crisis, the council is set to buy properties for its homeless in "less expensive areas" such as outer London boroughs.
A pot of £5m has been agreed to buy properties, both inside and outside the borough, to be used as temporary accommodation.
The borough is in the grip of a homelessness crisis as the number and size of homeless families soars due to sky-rocketing private rents up 14 per cent in a year and housing benefit cuts.
Lots of large, poor families who were in three, four or five-bedroom homes have been evicted by their landlords because they no longer get full housing benefit to pay rent.
Critics argue the council is not doing enough to solve the problem, which has seen the number of homeless families increase from 614 to 791 in the 12 months to March this year.
Only five families needed a four-bedroom flat in 2010 but this shot up to 68 last year.
Head of policy and campaigns for Crisis homeless charity, Katharine Sacks-Jones, said: "These shocking statistics are reflective of a city where, shamefully, rough sleeping has doubled in the past six years.
"Forcing people away from their communities, friends, families and support networks will leave them isolated and reduce their chances of keeping their job or finding new work.
"The Government needs to urgently consider the impact its cuts to housing benefit are having and together with the Mayor focus on building the genuinely affordable homes to rent we so badly need."
Wandsworth Council has been keeping large numbers of people in bed and breakfast accommodation, in one case for 38 weeks, which is well past the suggested limit of six weeks and is extremely expensive.
Council documents revealed an in-borough issue of an increasing number of evictions from the private rented sector of large families dependent on welfare benefit. End of private tenancy agreements accounted for 53 per cent of Wandsworth's homeless cases. Four years ago it was 13 per cent.
The council’s Annual Housing Resources and Commitments report said fewer landlords were willing to work with the council to prevent homelessness.
Councillor Simon Hogg, opposition speaker for the housing overview and scrutiny committee, said: "It's very sad. Rents went up an average 14 per cent last year. With pay freezes and housing benefit cuts, many local families can't keep up. The council saw this homeless crisis coming but hasn't done enough to deal with it.
"I've seen how homelessness affects children in Battersea and Tooting. It also makes it much harder for parents to hold down a job. If we take action now we can head off larger social problems a mile down the road."
A spokesman for Wandsworth Council said: "All councils in London are experiencing an increase in homeless cases. In Wandsworth the council has approved a wide ranging package of measures to address this issue and ensure that those people who are in genuine need receive help and support."
One woman, who asked to be known as Sandra, spoke out about her experience of being made homeless in the borough.
She lived in a privately-owned ex-council house, in Battersea, but had to leave when her landlord suddenly put the rent up from £250 a week to £450. She had just graduated from university, when the council told her to stay in the house until the bailiffs came.
Fortunately, temporary accommodation became available, three days before her eviction, so Sandra and her son, four, lived there for 11 months. The pair have since been rehomed in Wandsworth.
Sandra, who is a self-employed filmmaker, said: "After they put the rent up - the rent goes over the housing benefit cap. Some of the single mothers are not working because they are looking after small children. Then they can’t afford it.
"[The landlord] said that’s the price. Everything is going up now. You take it or leave it. It is very unsettling not knowing.
"You try your best to find something but you are powerless."