The government’s two-child limit on benefits is having a devastating impact on family life as it pushes millions of children deeper into poverty, according to the first detailed study of the benefit cut.

Nearly all families affected by the limit reported cutting back on essentials such as food, medication, heating and clothing as a result of the policy, which makes them miss out on at least £53 a week in benefits support.

Many parents reported stress and strained family relationships, as well as shame and guilt at being unable to provide for their children. Several women said they had considered terminations because of fears over the impact on family finances.

Interviews with women experiencing domestic abuse suggested that the two-child limit was regarded as a financial barrier for women and children trying to escape an abusive relationship and created “stark choices between poverty and safety”.

The limit, introduced in April 2017, restricts the child element in universal credit and tax credits worth £2,780 per child per year to the first two children. The government has championed the policy, which will cut the benefits bill by £1bn a year by 2021, as an incentive for people on benefits to work.

However, official figures show most families affected are already in work, while the study found those affected felt strongly that the two-child limit unfairly punished hard-working low income families at a time – the birth of a child – when they most needed support.

One mother told researchers: “The safety net doesn’t exist any more for my family … You feel really distressed that you have turned to the welfare state and that there is nothing available for you and now I must turn to charity. What am I paying taxes for?”

Alison Garnham, the chief executive of Child Poverty Action Group, which published the report along with the Church of England, called for the two-child limit to be abolished. “We wouldn’t turn away a sick child from our hospitals or stop them going to school and yet the two-child limit denies families the support they need from our social security system when they experience tough times, trapping kids in poverty,” she said.

The limit will push an additional 300,000 children into poverty by 2024, while 1 million children already below the breadline will be pushed into deeper hardship, the report says. To date an estimated 160,000 families and 600,000 children have been affected, and this could rise to 1.8 million young people over the next five years.

Ministers have defended the policy on the basis that it forces parents to take responsibility for their choices and teaches them that “children cost money”. However, the study says the policy has been barely publicised by government, and only half those affected were aware of it before they became pregnant.

Many women interviewed said their third child had been unplanned. For them, the study noted, “the only way to exercise choice would have been to have a termination, which some of the women simply would not contemplate for moral or emotional reasons and which those in Northern Ireland would have been unable to access even if they had wanted to.”

Relatively few claimants appeared to have used a “rape clause” covering a third or subsequent child conceived as a result of sexual assault.

The report dismantles a claim made by the policy’s supporters that claimants could compensate for the cut in support by getting a job or working more hours. Nearly three in five (59%) families affected are already in work, while analysis for the report showed it was impossible for most affected families to make up the loss through extra hours.

“The overriding picture emerging from both the survey and interview findings is that families affected by the two-child limit are facing severe and ongoing financial difficulty, which cannot be overcome through careful budgeting or just ‘tightening their belts’, but instead leads to real deprivation,” the report says.

The policy disproportionately affects the most deprived areas. In two parliamentary constituencies – Bradford West and Birmingham Hodge Hill – more than 50% of children could potentially be affected, while in a further 37 constituencies the proportion is more than a third.

A government spokesperson said: “This policy helps to ensure fairness by asking parents receiving benefits to face the same financial choices as those in work. Safeguards are in place and we’ve made changes this year to make the policy fairer.”

This year the government cancelled much-criticised plans to extend the two-child policy in universal credit to children born before the policy was introduced. It exempted kinship carers after the high court found last year that the policy as it affected this group was “perverse and unlawful”.