Jeremy Corbyn is dropping the idea of social mobility as a goal for the next Labour government, saying he would instead create a “social justice commission” with the power to audit policy.

In a shift being billed by Labour strategists as the rejection of 40 years of political consensus, Corbyn said on Saturday that pursuing social mobility “has failed, even on its own terms”.

Speaking at a Labour education event in Birmingham, the party leader vowed to replace the idea that the brightest, most talented young people must have the opportunity to succeed, with a demand that all children be allowed to flourish.

“For decades we’ve been told that inequality doesn’t matter because the education system will allow talented and hard-working people to succeed whatever their background. But the greater inequality has become, the more entrenched it has become,” he is expected to say.

“The idea that only a few talented or lucky people deserve to escape the disadvantage they were born into, leaving in place a social hierarchy in which millions are consigned to the scrap heap, results in the talents of millions of children being squandered.”

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Labour would replace the social mobility commission, which is chaired by Dame Martina Milburn, with a social justice commission, the party said.

The watchdog would publish “social justice impact assessments” of government policies – including green papers, white papers and legislation. It would also publish advice to ministers about how best to pursue social justice.

Responding to questions about what a social justice commission would do that a social mobility commission has not, Corbyn said: “It’s going to make sure that we get an education system that makes sure all of our children achieve their best in school.

“The idea of social mobility where you pluck somebody out of poverty and promote them into a private school education or promote them somewhere else doesn’t actually help the majority. What we have is a lot of under-used talent in society.

“A social justice commission will be there to make proposals, ask very tough questions of government and will measure our government against the improvements in social mobility for the entire population, not just the few.”

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Corbyn’s move is the latest evidence of his team’s determination to reshape Labour – and underlines his belief that the Tony Blair and Gordon Brown governments did not do enough to shake up the economic system.

Enhancing social mobility has been the aim of governments on both sides of the political divide. Blair’s close ally Peter Mandelson memorably said he was “intensely relaxed about people getting filthy rich as long as they pay their taxes” – though he has since admitted he has become more concerned about inequality.

Labour is keen to show that its thinking has developed since Corbyn and his advisers drew up the 2017 general election manifesto.

Theresa May made it her goal shortly after becoming prime minister to create a “great meritocracy” in Britain, not least by expanding grammar schools – a policy that was quietly dropped after the Tories lost their majority in 2017.

At the Birmingham event the shadow education secretary, Angela Rayner, said: “Focusing only on a lucky few leaves inequality entrenched and those from disadvantaged backgrounds with few opportunities to get on. That was the damning verdict of the government’s own social mobility commission, which Tory ministers have shamefully ignored.”

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She embraced the legacy of past Labour governments, saying: “The Tories like to talk about people like me who had a difficult start but got on in life as evidence that anyone can succeed on their own. But actually my life shows the exact opposite. Any success I have had is thanks to Labour governments that provided the council house, minimum wage, tax credits and Sure Start children’s centre that enabled me to achieve it. That is social justice.”

The social mobility commission was set up by David Cameron’s coalition government. Its most recent report found that inequality is “now entrenched from birth to work”, with social mobility stagnating “at virtually all life stages” over the past five years.