Video report by ITV News Political Correspondent Emily Morgan
Theresa May is facing fresh pressure after it emerged her entire social mobility commission is quitting over the government's failure to make good on its promises to build "a fairer Britain".
Alan Milburn, the former Labour minister who heads the commission, told ITV News he had reached the conclusion the government had "little hope"of making the progress needed to tackle "searing divides".
"There’s only so long that you can go on pushing water uphill," he said.
"The government as a whole it’s become increasingly obvious, simply doesn’t have a plan to tackle the searing divides that scar the nation."
"We need a national strategy, national resources, and we need a huge amount of effort and a far bigger ambition than is being applied at the moment," he added.
Mr Milburn also said he now plans to set up his own social mobility institute .
In a resignation letter first seen by the Observer, Mr Milburn wrote that intense focus on Brexit means the Government "does not seem to have the necessary bandwidth to ensure the rhetoric of healing social division is matched with the reality".
Mr Milburn also told the newspaper pledging change and then failing to follow it through was the "worst position" and it would be "almost better" never to promise improvements.
"It means more anger, more resentment, and creates a breeding round for populism," he added.
Three other commissioners at the body, including the Conservative former cabinet minister Baroness Shephard, are also resigning.
A government spokesman said the resignations came after Mr Milburn - whose term expired last July - was told that a new chair was to be appointed and an open application process would be held for the role.
Mr Milburn said his reappointment for a second term as commission chair had been backed by Education Secretary Justine Greening but she had failed to prevail in Whitehall.
"She was trying to secure my reappointment with Number 10 that didn't work for whatever reason," he told ITV News.
"She told me they’d be an open appointment and I’ve decided I’m not applying for the job," he added.
Ms Greening told the BBC's Andrew Marr Show, she was not going to "get into the discussions we have inside Government" but that Mr Milburn had done a "fantastic job".
She added: "But his term had come to an end and I think it was about getting some fresh blood into the commission."
The resignation of Mr Milburn and his colleagues will add to pressure on Mrs May, who has made commitments to build a fairer society a cornerstone of her offer to voters.
It comes just days after the commission warned that unless the economic, social and local divisions laid bare by the Brexit vote were addressed there would be a rise in far right or hard left extremism.
However, a government spokesman said the resignations came after Mr Milburn - whose term as commission chair expired last July - was told that a new chair was to be appointed and that an open application process would be held for the role.
The government spokesman said: "We are extremely grateful to Alan Milburn for his work as chair of the Social Mobility Commission over the past five years."
"This Government is committed to fighting injustice and ensuring everyone has the opportunity to go as far as their talents will take them.
"We are making good progress with social mobility - we have increased the national living wage, cut income tax for the lowest paid and doubled free childcare.
"We accept there is more to do and that is why we are focusing our efforts in disadvantaged areas where we can make the biggest difference."
The prime minister is also facing a potential Brexit clash within her party as anti-EU MPs said she must refuse to pay the divorce bill if talks do not move forward to the next stage this month.
Prominent Tories including Jacob Rees-Mogg, John Redwood and former chancellor Lord Lawson signed a letter her to walk away from talks if EU leaders do not agree to a series of new demands.
These include settling the terms of a free trade agreement "in principle" by the end of March 2018 and an end to the jurisdiction of the European Court of Justice and the freedom of movement to the UK for EU nationals when the UK leaves a year later on March 30 2019.
The letter was organised by the Leave Means Leave group. Other signatories include Conservative former ministers Owen Paterson and David Jones and the Labour MP Graham Stringer.