The board of the government's Social Mobility Commission has stood down in protest at the lack of progress towards a "fairer Britain".
Ex-Labour minister Alan Milburn, who chairs the commission, said he had "little hope" the current government could make the "necessary progress".
Tory former cabinet minister Baroness Shephard is among three others to quit.
In a resignation letter first reported by the Observer, Mr Milburn said ministers were preoccupied with Brexit.
He said that meant the government "does not have the necessary bandwidth to ensure the rhetoric of healing social division is matched with the reality".
Mr Milburn added: "It seems unable to commit to the future of the commission as an independent body or to give due priority to the social mobility challenge facing our nation."
He took up his role with the commission, which monitors progress towards improving social mobility in the UK, and promotes social mobility in England, in July 2012.
'Unable to commit'
The resignations come as Theresa May, who entered Downing Street in July 2016 promising to tackle the "burning injustices" that hold back poorer people, faces questions over the future of senior minister Damian Green – who is effectively her second in command – and is under pressure as Brexit talks continue.
In his resignation letter addressed to Mrs May, Mr Milburn said he was standing down with "much sadness" and was "deeply proud of the work the commission has done".
He said: "All the main political parties now espouse a Britain that is less elitist and more equal, while growing numbers of employers, universities, colleges, schools and councils have developed a shared determination to create a level playing field of opportunity in our country."
Mr Milburn added: "Individual ministers such as the secretary of state for education have shown a deep commitment to the issue.
"But it has become obvious that the government as a whole is unable to commit the same level of support…
"I do not doubt your personal belief in social justice, but I see little evidence of that being translated into meaningful action."
In a report published last week, the commission said economic, social and local divisions laid bare by the Brexit vote needed to be addressed to prevent a rise in far right or hard left extremism.
The commission added that London and its commuter belt appeared to be a "different country" to coastal, rural and former industrial areas as young people there faced lower pay and fewer top jobs.
Mr Milburn told the Observer: "The worst position in politics is to set out a proposition that you're going to heal social divisions and then do nothing about it. It's almost better never to say you'll do anything about it…
"In America for 30 years real average earnings have remained flat. Now here the Chancellor is predicting that will last for 20 years.
"That has a consequence for people, but a political consequence as well. It means more anger, more resentment and creates a breeding ground for populism."
In an interview in the Sunday Times, Mr Milburn, a former health secretary, said: "There has been indecision, dysfunctionality and a lack of leadership."
Downing Street is yet to respond to the board's announcement.
Shadow cabinet office minister Jon Trickett said the resignations came as "no surprise".
"As inequality has grown under the Tories, social mobility has totally stalled," he said. "How well people do in life is still based on class background rather than on talent or effort."