A key government welfare reform designed to motivate people into work is leaving families with mounting debt and pushing poor children into deeper poverty, according to analysis seen by the Observer.

Two-thirds of the households stuck in the government’s benefit cap for more than six months were found to be facing a shortfall between their monthly income and estimated costs, suggesting the policy is fuelling destitution.

The study of more than 10,000 benefit-capped households by the Policy in Practice consultancy found that for every child whose parents move back into work as a result of the cap, eight more will grow up in families whose financial circumstances have worsened following the introduction of the policy.

More than half of the households affected by the benefit cap were left stuck on it for six months or more. The average gap between rent and housing benefit for families stuck on the cap was £3,750 a year.

Senior MPs said the analysis showed people were being “pushed to the brink of destitution” by a policy that was not working. The group of households stuck under the cap also includes disproportionate numbers of people requiring help due to illness or disability.

Theresa May is still under pressure over welfare despite a £1bn package in the budget to make the universal credit system more generous. The Resolution Foundation thinktank has found that three-quarters of the £12bn in welfare cuts announced after the 2015 election remain government policy.

Frank Field, the chair of the Commons work and pensions committee, said: “As with universal credit, the driver of this reform was meant to be getting people into work, and you can escape the cap if you do. But we know that for too many, especially those with young children, work simply doesn’t pay and is out of reach.

“If getting into work that pays isn’t a genuine, realistic possibility for each person affected by the cap, and they are as a result pushed to the brink of destitution, we must ask why, and ask also whether the cap should operate at all for this group.”

Further analysis by Policy in Practice, carried out on a sample of council tenants across 11 English local authorities, showed those stuck on the benefit cap are more likely to be in debt.

Tenants on the benefit cap were two-thirds more likely to be in rent arrears than all other tenants claiming housing benefits, while 28% of all households currently affected by the cap are in receipt of a discretionary housing payment – in effect extra help handed out by councils to people in trouble paying their rent.

The benefit cap was lowered in 2016 and limits the total amount of benefits a household can receive to a maximum of £20,000 a year, or £23,000 for families in London.

Policy in Practice found that only 37% of those who escaped the cap did so due to a higher income. While it estimated that the policy had increased the likelihood of moving into work by 21%, it suggested there was a major social impact.

Deven Ghelani, the director of Policy in Practice, said: “I have always been open to this policy having a positive impact for those families moving into work. However, our analysis shows that the positive employment outcomes and savings generated do not appear to offset the financial costs, or crucially, the human and social costs associated with rising levels of economic destitution.”

Chris Goulden, the deputy director at the Joseph Rowntree Foundation, said work was the best route out of poverty for most people, but those with limited options because of their health or disability could be unfairly affected.

“With the high and rising cost of housing, especially in the capital, these shortfalls in income can lead to a rising tide of debt as people struggle to find ways to stay afloat that don’t end up worsening their situation,” he said. “The benefit cap is a clumsy solution to a real problem caused by high rents, low paid work and barriers to engaging in paid work among groups like disabled people.”

The Department for Work and Pensions said official statistics showed that seven in 10 households came off the cap eventually. It said help was being provided to single parents looking for appropriate work, and around 54,000 households were no longer subject to the cap.

Esther McVey, the work and pensions secretary, said: “The benefit cap ensures we have a fairer system – fair for the taxpayer and fair for claimants – as well as a system that incentivises work. So it’s not surprising that we now have the lowest unemployment figures since 1975.”