An extra 250,000 children will be hit by the two-child benefit cap next year, rising to an extra half a million by 2029, a leading thinktank has warned.

The Institute for Fiscal Studies (IFS) said the number of children who will fall under the cap – which limits child benefits for the first two children in most households – will reach 670,000 by the end of the next parliament if the policy is not reformed.

The two-child benefit cap, which restricts Child Tax Credit and Universal Credit to the first two children, was brought in by the Conservative government in 2017.

Campaigners have long called for it to be abolished on the grounds it would lift thousands of children out of poverty.

It comes as a separate study from the Joseph Rowntree Foundation (JRF) found 40% of people who work in primary schools and GP surgeries have considered quitting their job because of a “shameful” level of hardship among the population.

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The JRF found the service providers were “staggering under the weight of hardship” by having to provide extra support to the nearly four million people struggling to pay for essentials including food, heating and clothing.

The IFS said the two-child cap has helped drive up the share of children in large families who are in relative poverty from 35% in 2014-15 to 46% in 2022 – a period when poverty for families with one or two children fell.

The Labour Party has faced pressure to drop the cap – including from former prime minister Gordon Brown – but has so far refused to commit to ending it, citing the current state of the country’s finances.

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The pressure intensified further after figures on the right, including former home secretary Suella Braverman and Reform leader Nigel Farage, both called for the cap to be scrapped.

Abolishing the cap does not appear in either the Tory or Labour manifestos, with only the Green Party and Liberal Democrats making the commitment in their offers to the public.

The IFS said removing the cost of the limit would cost the government about £3.4bn a year, equivalent to freezing fuel duties for the next parliament.

The limit currently affects two million children and more children are added each year because it applies to those born after 5 April 2017.

The IFS said when fully rolled out, the cap will affect one in five children, rising to 38% of those in the poorest fifth of households.

It said 43% of children in households with at least one person of Bangladeshi or Pakistani origin will be affected, while those who fall under it on average will lose £4,300 per year – representing 10% of their income.

IFS research economist Eduin Latimer said: “The two-child limit is one of the most significant welfare cuts since 2010 and, unlike many of those cuts, it becomes more important each year as it is rolled out to more families.”

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Mubin Haq, chief executive of the abrdn Financial Fairness Trust, which funded the research, said: “The limit has been a significant contributor to child poverty amongst large families during a period when poverty for families with one or two children fell.

“If the next government is serious about tackling child poverty, it will need to review the two-child limit.”

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Alison Garnham, the chief executive of Child Poverty Action Group, said the “biggest driver” of child poverty in the UK was the two-child limit.

“Any government serious about making things better for the next generation will have to scrap the two-child limit, and do so quickly.”

A Labour spokesperson said: “We are under no illusions about the scale of the task ahead if we win the election.

“Labour has already set out how we would make a start, with free breakfast clubs in every primary school, cutting fuel poverty and bringing down energy bills, banning exploitative zero hours contracts, making work pay, ending no-fault evictions and creating more good jobs right across the country.”