The Government's so-called "benefit cap" is threatening to cause severe hardship to some of the most vulnerable people in society, the Court of Appeal has been told.
The flagship policy is having a particularly harsh impact on women fleeing domestic violence, and on their children, three senior judges heard.
Two lone parents forced into temporary accommodation in London, and one each of their children, are asking the appeal court to rule in test cases that the cap regulations violate human rights laws and the common law.
As their appeals started at the Royal Courts of Justice in London, anti-cap demonstrators outside the building called out: "Not bad women - just bad laws".
Rebekah Carrier, solicitor for both mothers, who are from Hackney and Haringey, said the court had 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 Goverment claim that families hit by a loss of benefits would be protected by additional funding through discretionary housing payments (DHPs) was misleading because DHPs were only short-term solutions.
Today's challenges are to the lawfulness of a 2012 amendment to the Housing Benefit Regulations, used by Work and Pensions Secretary Iain Duncan Smith to introduce the cap.
The cap formed part of Government reforms to reduce spending on welfare by £11 billion per year.
A Department for Work and Pensions (DWP) spokeswoman said in a statement: "We remain confident that the benefit cap measures are lawful.
"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."
Ian Wise QC, for the families, told the court the secretary of state had "failed to ask himself the right questions and obtain relevant information concerning the impact of the scheme on those escaping domestic violence and regarding temporary accommodation".
The cap generally affects housing benefit, child benefit and child tax credit paid 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.
Both the Child Poverty Action Group (CPAG) and Shelter children's legal centre are making submissions during the two-day hearing.
The CPAG says the cap cannot be justified by the need to make fiscal savings, given its "disproportionate impact on women".
A third mother in temporary housing has dropped out of the hearing, having secured a council flat in the borough of Hammersmith and Fulham after being on a waiting list for over five years and no longer affected by the cap.
Mr Wise submitted: "The perverse effect of the cap in her case has been to enable her to 'jump the queue' for a council property as a result of the operation of the cap."
He said of the two families still in the legal challenge: "Both families have been subject to physical and sexual abuse - there is copious evidence of that."
He told Lord Dyson, Master of the Rolls, sitting with Lord Justice Longmore and Lord Justice Lloyd Jones, they faced "loss of their homes, destitution and increased risk of violence".
One of the mothers, referred to as "MG", was receiving £75 a week less in benefits while "SG" had a £50 reduction because of the cap.
Mr Wise said: "It is important to realise these reductions are such that they bring the families to being on or below destitution levels."
The appeal is against a High Court ruling last November. Two judges found that, even though the families were "particularly hard cases", the 2006 regulations did not breach human rights laws and were not disproportionate.
Mr Wise submitted the High Court had "gone wrong in law" and the families were being discriminated against in breach of Article 14 of the European Convention on Human Rights.
The cap also amounted to "an unjustified interference" with their Article 8 rights to private and family life.