The news is a blow to Prime Minister Theresa May, who has promised to make tackling social injustice a priority for her Conservative government. On her first day in office in July 2016, May vowed to "do everything we can to help anybody, whatever your background, to go as far as your talents will take you."
But since then much of the government's time and energy has been spent on divorce negotiations with the European Union and preparing for Brexit in March 2019.
Former Labour government minister Alan Milburn and three fellow commissioners have all resigned from the Social Mobility Commission. They include Gillian Shephard, a former Conservative government minister.
In a resignation letter, Milburn said that the focus on Brexit means the government "does not have the necessary bandwidth to ensure the rhetoric of healing social division is matched with the reality."
"There's only so much you can do to push water up a hill," Milburn told Sky News on Sunday.
In a report released last week, the commission said that stagnating real wages and a growing gap between the prosperous London region and the rest of the country were a recipe for anger and "a breeding ground for populism."
The government said Milburn's term in office has ended and he was due to be replaced.
It insists it is making progress toward a fairer society, pointing to increases in the minimum wage, tax cuts for low earners and expansion of free childcare.
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