Benefit caps hit hundreds of families in Kensington and Chelsea over the last six years, figures show.
Charities warned the caps have added to the misery of families teetering on the poverty line, with most of those affected having children.
Department for Work and Pensions figures show that 1,521 families had their housing benefits capped in Kensington and Chelsea between the introduction of the limits in April 2013 and February this year.
Single parents accounted for nearly half of the capped claimants, 46% of cases.
Greg Beales, the campaign director for housing charity Shelter, said that benefit capping was pushing people towards homelessness, with single-parent families disproportionately affected.
He added: “When your benefits can’t cover both rent and food you end up having to choose between the two.
“Lone parent families tell us how they can’t afford to feed themselves and their children, let alone cover childcare and think about returning to work. The system is entirely self-defeating.”
Scrapping the cap, raising housing benefit rates and fixing structural issues that “push so many perilously close to the trauma of homelessness” would overhaul the system into one fit for purpose, he argued.
In London, couples with children are limited to an annual income from all benefits of £23,000 a year, £442 each week. The cap is lower outside the capital, at £20,000.
Single adults and lone parents whose children do not live with them have lower limits. Some people are exempt from the cap, such as those receiving tax credits or claiming carer’s or guardian’s allowances.
Over the six-year period, 313 households in Kensington and Chelsea were docked more than £100 a week. Of those, 107 saw more than £200 a week capped.
More than 204,000 households in Great Britain have had their benefits capped since the limit was brought in, 62% of whom were single-parent families. These include 60,570 in London, where single-parent families accounted for 59% of cases.
In February, when the most recent data was available, 263 families still had their benefits capped in Kensington and Chelsea. When the cap was lowered to its present level in November 2016, there were 257.
The chief executive of the Child Poverty Action Group charity, Alison Garnham, said the statistics “expose the absurdity and incoherence” of the benefit cap policy.
The “arbitrary” limit punished single parents with young children for being unable to work, giving them insufficient financial support to live on, she added.
She said: “The losses these families sustain as a result of the cap are stark and do nothing to improve parents’ chances of moving into work when they are able to.
“Our social security system should be there for people when they need it most and this is just one example of a number of harsh measures that together keep children trapped in poverty, unable to enjoy a childhood full of opportunity and free of disadvantage.”
A spokesman for the DWP said: “The benefit cap provides fairness to the taxpayer while ensuring there’s a safety net for the most vulnerable.
“Working is the best route towards prosperity and the benefit cap provides a clear incentive. More than 60,000 households have moved off the benefit cap due to starting a job or increasing their hours.”
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