Two judges are being asked to rule that new capping regulations introduced by Work and Pensions Secretary Iain Duncan Smith are "unlawful" and breach the human rights of out-of-work women struggling to bring up families on their own.
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 three mothers and one child from each family, all from the London area, say the "cruel and arbitrary" measure is "reminiscent of the days of the workhouse", and the women fear it will leave them destitute.
But the Department for Work and Pensions (DWP) argues the cap is "manifestly justifiable to make savings, and seek to reduce the fiscal deficit, by capping benefits at the level of average earnings".
A DWP spokesman said: "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."
The mothers are asking 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 capping would result in families receiving state assistance "below destitution levels" and less than that afforded to asylum seekers.
Rebekah Carrier, solicitor acting for the claimants, who come from the boroughs of Hackney, Haringey, and Hammersmith & Fulham, said: "This is a cruel and arbitrary policy."
Ms Carrier, from law firm Hopkin Murray Beskine, said the first cappings she had seen under the new policy had begun in October.
She said the DWP claim that families hit by a loss of benefits would be protected by additional funding through discretionary housing payments (DHPs) was misleading as DHPs were only short-term solutions.
The legal challenge is being supported by the Child Poverty Action Group and the Women's Aid Federation.
They warn the "unjustifiable" 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.