Three single mothers and their children, including one from an Orthodox Jewish family in north London, plan to appeal over a “disappointing” High Court decision that the Government’s flagship “benefit cap” policy is lawful.

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The new cap affects housing benefit, child benefit and child tax credit to families who do not work sufficient hours to qualify for working tax credit, and is set at £500 per week for couples or lone parents.

Two judges accepted the mothers had “particularly hard cases”, but new capping regulations introduced by Work and Pensions Secretary Iain Duncan Smith did not breach human rights laws and were not disproportionate.

The Jewish woman, known only as “SG”, has six children, three of whom aged three to nine are living with her. She has also fled alleged sexual and physical violence.

Lord Justice Elias and Mr Justice Bean, sitting in London, declared in a joint judgment that it was not for the court to interfere with a Government policy aimed at reducing long-term dependency on benefits and encouraging people into work.

The capping affects housing benefit, child benefit and child tax credit to families who do not work sufficient hours to qualify for working tax credit, and is set at £500 per week for couples or lone parents.

Lawyers acting for the mothers and one child from each family, all from the London area, said the “cruel and arbitrary” measure is “reminiscent of the days of the workhouse”, and the women fear it will leave them destitute.

Dismissing the claim for judicial review, the judges said many considered the cap to be “too parsimonious”.

They ruled: “But that is ultimately a policy issue, and for the reasons we have given we do not think it can be said that the scheme is so manifestly unfair or disproportionate as to justify an interference by the courts.”

Rebekah Carrier, solicitor acting for the claimants, who come from the boroughs of Hackney, Haringey, and Hammersmith & Fulham, said: “We are disappointed by this judgment. Two of the claimant families had fled domestic violence. The court failed to grapple with the difficulties caused by the way that women seeking a safe space for themselves and their children are charged for their accommodation, including in women’s refuges.”

The mothers’ legal challenge was supported by the Child Poverty Action Group, Shelter and the Women’s Aid Federation.

Ms Carrier, from law firm Hopkin Murray Beskine, said the first cappings she had seen under the new policy started in October.

She said: “It is shocking that Government ministers failed to ensure they were properly informed about how the cap would actually work in practice and the adverse impact on lone parents, victims of domestic violence and children. The claimants intend to take this challenge to the Court of Appeal.”

The other two mothers who brought the challenge include “MG”, a member of the Roma community who fled Poland 16 years ago and was granted refugee status in the UK and a mother of five who is illiterate, speaks no English, she is a “devout” Roman Catholic and believes contraception “to be against the will of God”.