Four working single mothers have won a legal victory that could force the government to radically overhaul the way it operates the controversial universal credit scheme.

Two high court judges ruled the Department for Work and Pensions (DWP) was wrongly interpreting universal credit regulations after the women – who had argued they were struggling financially because of how the welfare system worked – were successful in their judicial review.

The women had argued a “fundamental problem” with the scheme meant their monthly payments varied enormously and they had ended up out of pocket, a problem their lawyers said was likely to affect tens of thousands of people.

Quick Guide What is universal credit and what are the problems? Show What is universal credit? Universal credit (UC) is the supposed flagship reform of the benefits system, rolling together six benefits into one, online-only system. The theoretical aim, for which there was general support across the political spectrum, was to simplify the system and increase the incentives for people to move off benefits into work. About 2 million people are currently in receipt of UC. More than 6 million will be on the benefit by the time it is fully rolled out. How long has it been around? The project was legislated for in 2011 under the auspices of its most vocal champion, Conservative MP Iain Duncan Smith. The plan was to roll it out by 2017. However, a series of management failures, expensive IT blunders and design faults mean it is now seven years behind schedule, and rollout will not be complete until 2024. The government admitted that the delay was caused in part by claimants being too scared to sign up to the new benefit. What is the biggest problem? The original design set out a minimum 42-day wait for a first payment to claimants when they moved to UC (in practice this is often up to 60 days). After sustained pressure, the government announced in the autumn 2017 budget that the wait would be reduced to 35 days from February 2018. This will partially mitigate the impact on many claimants of having no income for six weeks. The wait has led to rent arrears and evictions, hunger (food banks in UC areas report notable increases in referrals), use of expensive credit and mental distress. Ministers have expanded the availability of hardship loans (now repayable over a year) to help new claimants while they wait for payment. Housing benefit will now continue for an extra two weeks after the start of a UC claim. However, critics say the five-week wait is still too long and want it reduced to two or three weeks. Are there other problems? Plenty. Multibillion-pound cuts to work allowances imposed by the former chancellor George Osborne mean UC is far less generous than originally envisaged. According to the Resolution Foundation thinktank, about 2.5m low-income working households will be more than £1,000 a year worse off when they move to UC, reducing work incentives.

Landlords are worried that the level of rent arrears accrued by tenants on UC could lead to a rise in evictions. It's also not very user-friendly: claimants complain the system is complex, unreliable and difficult to manage, particularly if you have no internet access.

And there is concern that UC cannot deliver key promises: a critical study found it does not deliver savings, cannot prove it gets more people into work, and has plunged vulnerable claimants into hardship.

A DWP spokesman said: “We are carefully considering the court’s judgment.”

If the department chooses not to appeal then the women and their supporters expect to see almost immediate changes to the implementation of the scheme, which was introduced to replace means-tested welfare including income support and housing benefit.

Crucially, the changes would involve civil servants stepping in to manually override the automated way in which universal credit awards are calculated, a scenario the DWP had argued would be too costly and go against its design.

The ruling upstaged an announcement by the work and pensions secretary, Amber Rudd, of her plans to scrap a proposal to extend the two-child benefits cap, as part of an attempt to reset public perceptions of universal credit.

News of the ruling came in the middle of Rudd’s speech, in which she had described universal credit as a “fair and compassionate welfare system”.

Lawyers for Danielle Johnson, Claire Woods, Erin Barrett and Katie Stewart had challenged the method used by the DWP when calculating the amount payable under the 2013 universal credit regulations.

Lord Justice Singh and Mr Justice Lewis gave their ruling following a hearing in November, when they were told the women were struggling to manage their household budgets and some had fallen into debt or had to rely on food banks.

Lawyers for the women, whose case was brought by Leigh Day and the Child Poverty Action Group (CPAG), said the problem would arise when claimants were paid by employers on a date that clashed with their assessment period for universal credit.

The women pointed out that if a claimant were paid early because of a weekend or bank holiday, for example, the system would count them as having been paid twice in one month and they would receive a “vastly reduced” universal credit payment.

Amber Rudd, the work and pensions secretary, announces proposed changes to universal credit during a speech in London on Friday. Photograph: Yui Mok/PA

The judges said they had concluded the DWP had wrongly interpreted the relevant regulations. The interpretation was described by the judges as “odd in the extreme” and “could be said to lead to nonsensical situations”.

The ruling has immediate implications for the women. Barrett, who has a four-year-old son and was in hospital on Friday having her second child when the ruling was published, has been forced to stay with the same employer in York and to go to food banks.

Carla Clarke, a solicitor for the CPAG, who welcomed the “commonsense judgment”, said: “Food banks provide a valuable service, but one issue, for example, has been that she is a pregnant lady and needs access to fresh food and vegetables, as well as the ability to send her young son to nursery with a proper packed lunch.

“Working parents on low incomes should not lose out on the support that parliament intended them to receive because the DWP has designed a rigid process that is out of step with both actual reality and the law.

“Our clients have been doing everything they can to support themselves and their young children through work, but the rigid assessment system in universal credit has caused them untold hardship, stress and misery … being forced repeatedly to manage on half of their usual total monthly income despite their fixed outgoings remaining the same. They have each ultimately questioned why they are even working.”

Stewart, who has a two-year old daughter and has struggled to pay rent, resigned because she could not cope with what Clarke described as the “stress and anxiety of a constantly fluctuating UC system”, even though her outgoings were the same.

Tessa Gregory, a solicitor from Leigh Day who represented Johnson, said: “My client is a hardworking single mum doing her very best to support her family.

“She is precisely the kind of person universal credit was supposed to help, yet the DWP designed a rigid income assessment system which left her £500 out of pocket over the year and spiralling into debt due to a fluctuating income.”

The amount lost, as in the case of other women involved, equated to as much as a month’s rent, and the situation had left Johnson questioning whether she should stay in work or opt for the “stability” of being unemployed, even though she wanted to have a job.

Lawyers for the women have suggested that the ruling could affect potentially hundreds of thousands of UC claimants as the full scheme is rolled out.

David Finch, a senior research fellow at the Resolution Foundation thinktank, said: “It’s impact will go well beyond the limited number of people directly involved in the case, or even those with similar circumstances, because the judgment raises questions about how the core approach of monthly assessment periods with payment in arrears operates.”

A decision by the DWP regarding a possible appeal is expected to come on or before a hearing that has been provisionally scheduled for 26 February, to discuss costs and the question of compensation.