More than 300,000 poorer children will be hit by a new benefit cap coming in next week, a new study warns – with some families set to lose more than £100 a week.

The Government is being urged to rethink a dramatic lowering of the controversial household limit on social security payments, or face a devastating surge in poverty and homelessness.

The lower cap – £23,000 in London and £20,000 outside the capital – was announced by George Osborne last year, but will not come into force until next Monday, just weeks before Christmas.

Now research by the Chartered Institute of Housing (CIH) has found the numbers who will be affected is significantly higher than the Government expects. Pressing ahead will fly in the face of Theresa May’s promise, in her Conservative conference speech last month, to “make society fairer for families”, it warned.

Terrie Alafat, the CIH chief executive, said: “Our analysis shows many families could be one redundancy or a period of ill health away from being in this situation.

“This could have a severe impact on these families, make housing in large sections of the country unaffordable and risk worsening what is already a growing homelessness problem.”

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And Imran Hussain, director of Policy at the Child Poverty Action Group, said: “A lower benefit cap is crueller and more damaging for children.

“The only way to escape the cap is to work a certain a number of hours but, as the Government itself recognises in the rest of the benefits system, this is practically impossible for those with children under school age. They are trapped with nowhere to go.

“Given the unaffordability of housing, as shown in this report, no family should have to make a choice on paying the rent or putting food on the table.”

The much lower benefits cap was announced by then Chancellor George Osborne last year, but has yet to come into force (PA)

The CIH research shows that:

* 116,000 families with between one and four children will be hit – a rise of almost 100,000 on the 20,000 already affected.

* Those families contain a total of 319,000 children.

* They will lose up to £115 a week – a loss they cannot absorb “by simply reducing their household spending”.

* A couple with three children will be left with £50.80 a week for housing costs – yet rent for a three-bedroom property in, for example, Leeds, is £151.50 a week.

Around 20,000 families are currently capped by an annual limit of £26,000 (or £500 a week) on total household benefits, introduced in 2013. The new, lower caps will therefore bring an explosion in the numbers affected – ahead of a predicted slowdown in the British economy next year, in the wake of the Brexit vote.

In August, an impact assessment by the Department for Work and Pensions (DWP) suggested that 244,000 children will be affected, with families losing an average of £60 a week.

Ministers insist the cap acts as an incentive for people on benefits to move into work, because no one who has a job has the limit imposed on them. However, that claim is strongly disputed by experts who say there is no strong evidence of that – and that people in poorer families move in and out of work for many reasons.

One Government-backed project found that benefit cuts made it harder for the unemployed to find work, because they were pushed further into poverty, housing insecurity, hunger and debt.

Some families have been forced to move home – but more are thought to have simply cut back on spending, run down savings, taken out debt, or fallen back on family or friends.

Charities say that two-thirds of households affected are unable to work because of sickness or disability, or because they have very young children. Others will be receiving Jobseeker’s Allowance, which requires them to look for work, prompting statisticians to argue they could have found jobs without the cap.

The lower caps – of £442 a week in London and £385 a week in the rest of the country – will be imposed on 7 November, replacing the £26,000 (or £500 a week) figure. The cut will hit families particularly hard with Christmas – a time when many already struggle with high expenses and subsequent debt – just eight weeks away.

Of the 116,000 families affected, 18,000 families are in London, 17,500 in the South-east, 13,000 in the North-west and 12,000 in both the West Midlands and the East of England, the CIH said.

Nearly 19,000 have four children, around 56,000 have three children and more than 33,000 have two.

But a DWP spokesman said it did not recognise the figures, arguing they did not take into account the people who will move into work as a result of being capped. He said: “Anyone eligible for working tax credits, carers allowance and most disability benefits are exempt from the cap.

“The benefit cap restores fairness to the system and the new limit will ensure the amount people on out-work-benefits can claim better reflects the circumstances of many working families in the country.