The government shakeup of the tax and benefits system will result in a further 400,000 children falling into relative poverty during this parliament, leaving Britain on course to miss legally binding targets to reduce child poverty by 2020, according to the Institute for Fiscal Studies.

In a bleak assessment of changes in the government's new social contract, the IFS said the number of children in absolute poverty in 2015 will rise by 500,000 to 3 million. Even worse, by 2020 3.3 million young people – almost one in four children – will find themselves in relative child poverty.

This is 2 million short of the 2020 target to reduce child poverty to 10% or less of all children, and represents an increase of 800,000 on the figures for 2011.

The IFS, the UK's leading public finance thinktank, warns: "Absolute and relative child poverty are forecast to be 23% and 24% in 2020–21 respectively. These compare with the targets of 5% and 10%, set out in the Child Poverty Act (2010).

"This would be the highest rate of absolute child poverty since 2001/02 and the highest rate of relative child poverty since 1999/2000."

A child is considered to be in relative poverty if he or she lives in a household whose income is below 60% of the average in that year, and in absolute poverty if he or she lives in a household whose real-terms income is below 60% of the 2010/11 average – a period set as a benchmark in this year's Child Poverty Act.

The IFS said that while the introduction of the coalition's universal credit scheme will "act to reduce both absolute and relative poverty" the effect will be swamped by the "large decline in real incomes across the income distribution" and the new slower system of uprating means-tested benefits.

The IFS warns that average income is expected to fall by around 7% in real terms – the largest three-year fall for 35 years – in the years just before the new welfare system is brought in.

This and the pegging of welfare payments to consumer price inflation rather than the quicker uplift of retail price inflation will "more than offset the impact on poverty of universal credit".

The coalition's reforms mark a decisive break with Labour's policy of hidden redistribution that saw significantly increased spending on benefits and tax credits for families with children.

Child poverty fell by nearly a quarter between 1998 and 2009, but this was still not enough for the government to hit its child poverty target to reduce it by half.

Paul Johnson, the director of the IFS, said that there were consequences in increasing spending on tax credits for "work incentives".

Noting that David Cameron in opposition had made speeches saying that "fighting relative poverty was a central policy goal" and "ending child poverty is central to improving child wellbeing", he said that there was now "a colossal gap between rhetoric and reality".

"Even if there were a huge increase in the resources made available, it is hard to see how child poverty could fall by enough to hit this supposedly legally binding target in just nine years," he told the Guardian.

Speaking on BBC Radio 4's Today programme, universities minister David Willetts defended the government's record, blaming the wider economic malaise for a drop in living standards.

"We've tried to hold down fuel duty …we're freezing council tax, we've increased the income tax allowance. We've tried to do the things that help," he said.

"But you can't ignore the basic rules of economics that when you inherit a situation where an economy has shrunk by 7%, the money isn't there. We're living with the consequences of a serious drop in the economy and that's feeding into living standards across the board."

Increasing the number of apprenticeships and making it easier for people to own their own homes were part of government efforts to help raise living standards, he said.

But campaigners described the report as "devastating", saying ministers were in denial about poverty. Alison Garnham, chief executive of Child Poverty Action Group, said: "This devastating report leaves the government's child poverty and social mobility strategies in jeopardy.

"Ministers seem to be in denial that, under current policies, their legacy threatens to be the worst poverty record of any government for a generation."

A Department for Work and Pensions spokesman said: "The IFS acknowledge that universal credit will substantially reduce child poverty. It will make work pay for the first time, tackling in-work poverty and lift over 1 million people, including 450,000 children, out of poverty.

"Our wide-ranging reforms will have a dynamic impact on some of the poorest families, encouraging people into work, many for the first time and improving the life chances of children at an early age."