More than 60 families living on the Southwark side of SE1 - and more in North Lambeth - will be affected by the cap on housing benefit to be introduced by the coalition government next year.
From April 2013 the housing benefit cap will be £350 per week for single people without children and £500 per week for all others, including couples, lone parents and couples with children.
According to data published last month, around 527 existing claimants across Southwark are expected to be affected by the cap – 61 of those in SE1.
On average, each affected household in SE1 will lose just over £3,000 a year in benefits.
"This cap will make some areas of the borough no-go areas for families on low incomes," warned Cllr Ian Wingfield, deputy leader of Southwark Council.
"It's punishing our very poorest families and children at a time when everyone is finding it tough to make ends meet.
"Simon Hughes admitted this change would tear apart families, right before he went and voted for it.
"It is yet more hypocrisy from the Lib Dem MP and an utter betrayal of the very poorest families and children in his constituency. Whose side is he on?"
Lambeth Council last week revealed that it expects 670 households in its borough to have their benefits capped, but it has not yet published breakdowns by ward or postcode.
This weekend former Lib Dem minister Sarah Teather told The Observer: "The policy was essentially conceived as a political device.
"It is simply not in the same league as other policies that are challenging in their consequences but done for a good purpose.
"I don't think it was even remotely conceived as a financial cost-cutting device. I think it was conceived as a political device to demonstrate whose side you are on."
In Southwark the council says it will contact those at risk of homelessness and offer them advice about how they can sustain their tenancy, debt and money management and a referral to the employment programme Southwark Works.