As the benefit cap forces Enfield families out of the borough, the council predicts more people will be faced with eviction and homelessness.
Figures obtained using Freedom of Information requests show families with children have been relocated using discretionary housing payments.
In the first two months after the benefit cap was introduced in Enfield, 15 families with 46 children were moved out of London.
Darren Johnson, London Assembly Green Party Member, said: “The Mayor of London has clearly failed to ensure families in Enfield don’t have to uproot their children because of the benefit cap.
“Rents are so high across London that it is becoming impossible for people on low incomes, working part-time or temporarily unemployed, to stay put and make ends meet.”
While Enfield Council says it is doing all it can to protect vulnerable families, Councillor Ahmet Oykener claims more trouble is afoot.
The cabinet member for housing said: "Although we do not know the long-term effect of the government's welfare benefit reforms on rent or migration to Enfield, we do know that rents are currently rising in the private sector as demand grows from those in and out of work, including benefits claimants being placed in Enfield by other boroughs.
“Enfield’s population has already increased by more than 36,000 since the 2001 census resulting in significantly increased demands for council services at a time of unprecedented spending cuts.
“Enfield Council anticipates a growing number of evictions and homeless applications as local people feel the effects of the government’s welfare benefit reforms, putting extra pressure on our already hard pressed services.”
The total loss of housing benefit in Enfield is more than £10million a year.
The authority says approximately 2,700 of Enfield families including an estimated 4,000 children are currently financially worse off as a result of government changes to housing benefit.
Cllr Oykener added: "Enfield Council is offering support to local people affected by the Government's welfare benefit reforms, helping them in whatever choices they make.
“The council has set up a joint taskforce with Job Centre Plus and the Citizen's Advice Bureau which is working with families affected by the benefit cap to explain what options are available to them and help them cope with the drop in benefit.
“The council does not have a programme of forced moves out of London for families affected by the total benefit cap, however where a family asks us to help them find more affordable accommodation, we will provide assistance.”
A spokeswoman for the Mayor of London Boris Johnson said: "While reform of the welfare system is long overdue the Mayor has worked hard to secure transitional arrangements, such as additional funding for councils, incentives for landlords to reduce rents and more time for existing claimants.
"He is also on track to deliver a record number of affordable homes, with 100,000 to be built over two terms and around £3billion invested to improve London’s housing. This, he believes, is the most positive way to influence the market, rather than measures such as controlled rents, which he has no power to introduce and are likely to deter investment in building new homes.”