Three single mothers and their children plan to appeal over a "disappointing" High Court decision that the Government's flagship "benefit cap" policy is lawful.
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.
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."
Later a DWP spokesman said: "We are very pleased that the court has ruled that the benefit cap complies with the European Convention on Human Rights.
"The benefit cap sets a fair limit to what people can expect to get from the welfare system, so that claimants cannot receive more than £500 a week, the average household earnings."
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."
She said a DWP claim that families hit by a loss of benefits would be protected by additional funding through discretionary housing payments (DHPs) was misleading because DHPs are only short-term solutions.
The mothers' legal challenge was supported by the Child Poverty Action Group, Shelter and the Women's Aid Federation.
Ms Carrier highlighted the judges' remarks that the court was "uncertain" whether the full impact of the cap on claimants in the position of the mothers " was ever fully appreciated by Parliament, or indeed anyone else".
The judges said James Eadie QC, appearing for the Government, had conceded that statistics relating to the differences between the income available to benefits claimants and those in work "were not apparently brought to anyone's attention, not even by the Child Poverty Action Group, which has formulated the information specifically for this hearing".
But the judges said there was no doubt there had been "a full appreciation that the comparison between the income of those on benefit and earnings for those in work inevitably meant that the latter would receive more money than the former".
The judges said that, although the three were "particularly hard cases", they were "not typical of the effect of the policy in the country as a whole".
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 three mothers and the youngest child from each family had asked the judges to rule that the cap unlawfully breaches the UN Convention on the Rights of the Child and the European Convention on Human Rights, which protects the right to respect for home and family life.
Ian Wise QC, appearing for the families, told the judges at a hearing last month that capping would result in families receiving state assistance "below destitution levels" and less than that afforded to asylum seekers.
Campaigners are warning that the cap threatens to reduce the income of poor mothers - especially those from ethnic and religious backgrounds with traditionally large families fleeing domestic violence - to a level that makes it impossible to provide adequate food, clothing and other essentials.
The 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.
A mother of five who is illiterate and speaks no English, she is a "devout" Roman Catholic and believes contraception "to be against the will of God".
She has been granted a DHP for 13 weeks but fears what will happen when the payments end.
The judges were told that she had lived with four of her five children, aged between 12 months and 15 years, in damp, rodent-infested accommodation in Fulham for five years after her husband left her.
Outside court, she said through an interpreter: "My number one priority in life is my children and the second is to bring them up as proper citizens of this country."
She said she "cannot imagine how I am going to manage" under the cap.
Another applicant is "NS", a mother of three daughters aged between three and 11 living in Haringey who, the court heard, fled "horrific" sexual and domestic violence and abuse from her husband.
She is living in a two-bedroom, privately rented flat which was the former matrimonial home before her husband was forced out by a court order.
The third mother is "SG", who is from an Orthodox Jewish family in north London. She has six children, three of whom aged three to nine are living with her. She has also fled alleged sexual and physical violence.
Ms Carrier said it was expected that the impact of the cap would be most acute in London because of the lack of affordable housing and high housing benefit costs.