Four women have launched a high court legal challenge to universal credit, arguing that an arbitrary design flaw in the payment system for the new benefit is “irrational and discriminatory” and leaves some families hundreds of pounds a year worse off.

They say the flaw, which relates to the way universal credit monthly payments are calculated, disproportionately affects working parents with children, though it is likely to affect tens of thousands of people claiming the benefit.

The women say the flaw leaves claimants with a “dramatically fluctuating income” and unable to budget from month to month. They can also suffer financial shortfalls because of what lawyers call a “rigid, inflexible assessment system”.

One of the women, Claire Woods, 30, said the cashflow problems caused by the fluctuating payments forced her to rely on a food bank and run up debts. She was subsequently forced to turn down a promotion and put her career on hold.

Woods said: “I invested £40,000 in higher education studies so that I could become an occupational therapist and it’s great that I’ve got my degree but I have had to put my career hopes on hold because of universal credit.

“I am competent, managing my own finances and am someone who wants to work for professional and personal development, but the assessment period problem meant my income fluctuated so much that it was impossible to budget.”

Another of the women, Danielle Johnson, 25, of Keighley, who works part time in a school kitchen and receives universal credit to top up her income, said she was £500 a year worse off as a result of the design flaw.

She said: “I have never been this financially unstable before, to the point of being unable to afford my rent and having to go into my overdraft when buying food. It is getting me into a vicious cycle of debt.

The problem arises when claimants’ wages are paid on or close to the first day of their universal credit monthly assessment period, which is used to calculate how much a claimant is entitled to be paid each month.

If a claimant is paid wages a day or two earlier – because their normal payday would fall on a weekend or bank holiday, for example – the system records them as having had two pay cheques in one assessment period and none in the following one.

As a result, universal credit considers them to be earning more than they actually do in the first period. In the second period it wrongly considers them to be earning nothing, meaning they lose out of work allowance of up to £258 each month.

Universal credit is a means-tested benefit that replaces other benefits including income support, jobseeker’s allowance and housing benefit. It is the second legal action on universal credit to reach the high court, following a ruling in June that the system unlawfully discriminated against severely disabled people.

In some cases uncovered by the Child Poverty Action Group (CPAG) , household income fluctuated wildly as a result of the design flaw. In one case, a family’s monthly payment swung from £1,185 to zero, making budgeting impossible.

Woods is represented by CPAG along with the other two claimants, Erin Barrett and Katie Stewart.

CPAG’s solicitor, Carla Clarke, said: “Universal credit is promoted as a benefit that incentivises work but in practice its rigid assessment period system undercuts that claim. Our clients have been left repeatedly without money for family essentials simply because of the date of their paydays.”

Tessa Gregory, a partner at the law firm Leigh Day, representing Johnson, said: “It is very clear through the multitude of problems reported that universal credit is a broken and ill-thought out system.”

The challenge against the Department for Work and Pensions opened on Tuesday at the high court in London. It is expected to last two days with a ruling expected next year.