The former Labour prime minister Gordon Brown will launch a scathing attack on the failure to deal with rapidly rising child poverty on Wednesday and warn that Britain is creating a generation of children whose sufferings are never talked about.

Speaking at the Edinburgh international book festival, Brown will say it is a national disgrace that the number of children living below the poverty line is set to rise to more than five million by the early 2020s.

Brown, who as chancellor used tax credits and benefit increases to boost the incomes of poor families during the Labour governments of 1997-2010, will say child poverty is heading towards “epidemic proportions”.

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Brown’s address at an event publicising his memoir My Life, Our Times will attack the deep cuts to tax credits and benefits announced by the former Conservative chancellor George Osborne in 2015, which have affected the wellbeing of low-income families at a time when wage increases have been modest.

“Child poverty is already the biggest social injustice of our generation and it appears to be accelerating out of control with child benefit and other child support still frozen or falling in value”, Brown says.

Brown cites a report for the Scottish government showing that child poverty was on course to almost double from 210,000 to 400,000, between 2010 – the year he lost the general election – and 2027.

The report found that almost two in five children in Scotland could be living below the poverty line – 60% of median income after taking account of housing costs – by the end of the next decade, and that measures taken by the SNP government at Holyrood would do little to counteract the impact of cuts decided at Westminster.

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Brown says the trend in Scotland will be replicated in the rest of the country, reversing the progress made in the 2000s.

“The majority of children in poverty will be in families where the breadwinner is in work – and not earning enough to escape poverty. Sadly in today’s gig and zero-hours economy, the old social contract – that if you worked hard you would make a decent living – no longer holds.”

“The prospects for nearly half a generation of children are in tatters, with governments shamefully ignoring this national disgrace – the silent suffering and sorrows of the left-out millions – and simply hoping the children, and the numbers, will remain invisible.”

Brown says that research by the Resolution Foundation thinktank shows that tax credits introduced by Labour reduced the number of children living in poverty in the UK from three million in 1998 to 1.6 million in 2010 – a bigger increase than shown by official figures due to the under-reporting of benefit payments.

He adds that studies have shown that the most effective way to tackle relative child poverty would be to combine a living wage and higher child benefits with tax credits that included a more generous element for children.

“We cannot keep ignoring child poverty. We cannot condemn almost half a generation to poverty.”