Nearly a quarter of a million children from poor families will be hit by the extended household benefit cap due to be introduced this autumn, according to the government’s latest analysis of the impact of the policy.

The new cap will take an average of £60 a week out of the incomes of affected households, almost certainly pushing them deeper into poverty. About 61% of those affected will be female lone parents.

Anti-poverty campaigners said the cap would damage the life chances of hundreds of thousands of children, and force already poor families to drastically cut back on the amount they spend on food, fuel and clothing.

The new cap restricts the total amount an individual household can receive in benefits to £23,000 a year in London (£442 a week) and £20,000 in the rest of the UK (£385 a week). It replaces the existing cap level of £26,000.

The Department for Work and Pensions (DWP) has argued that the benefit cap acts as an incentive for people on benefits to move into employment, because getting a job automatically exempts them from cap penalties.

It claims the cap makes people more likely to search for work, and says that 23,000 affected households have taken a job since its introduction in 2013. “The benefit cap restored fairness to the system by ending the days of limitless benefit claims and provides a clear incentive to move into work,” said a DWP spokesman.

However, an official evaluation of the cap by the Institute for Fiscal Studies in 2014 found the “large majority” of capped claimants did not respond by moving into work, and a DWP-backed study in Oxford published in June found that cutting benefit entitlements made it less likely that unemployed people would get a job.

Joanna Kennedy, chief executive of the charity Z2K, said: “Our experience helping those affected by the original cap shows that many of those families will have to reduce even further the amount they spend on feeding and clothing their children, and heating their home to avoid falling into rent arrears and facing eviction and homelessness.”

The chief executive of the Child Poverty Action Group, Alison Garnham, said: “A lower cap that cuts family budgets will do nothing to help parents who want to work. Instead it will damage the life chances of hundreds of thousands more children.”

Although the new lower cap levels mean the total number of those affected will rise, the latest impact assessment suggest this will be more modest than previous estimates. The new projection of 244,000 children affected is substantially less than the 330,000 figure contained in the DWP’s initial analysis, published in July 2015.

The DWP said the new lower figures – which also reduce the projected cash savings over the first four four full years of the cap by £400m – were explained by falling numbers of people claiming unemployment benefits and the introduction of exemptions for people claiming carer’s allowance and guardian’s allowance.

The government was in effect ordered to exempt carers after a judge ruled last year that it unlawfully discriminated against disabled people by capping benefits for relatives who cared for them full time. Ministers had argued that carers who looked after family members for upwards of 35 hours a week should be treated as unemployed.

A previous court ruling found that the benefit cap breached the UK’s obligations on international children’s rights because the draconian cuts to household income it produced left families unable to clothe and feed themselves.

The deputy president of the supreme court, Lady Hale, said in her judgment: “Claimants affected by the cap will, by definition, not receive the sums of money which the state deems necessary for them adequately to house, feed, clothe and warm themselves and their children.”