The entire board of Britain's cross-party social mobility commission has resigned, citing a lack of "political leadership" to address injustices in living standards and opportunities.

Alan Milburn — a former minister for the opposition Labour Party, who chairs the unit — is stepping down, along with the three other commissioners, the Observer newspaper reported on Sunday.

Milburn said with Brexit on the horizon, there was "little hope" of British Prime Minister Theresa May delivering on a promise made when she took office last year to address the "burning injustices" in British society.

Uncertain future

The resignations follow several reports suggesting that Britons can expect living standards to continue falling over the next 20 years, a decade after the 2007/8 financial crisis forced the government into a program of deep austerity.

In his resignation letter, Milburn accused the government of being too fixated on leaving the European Union to improve the prospects of those from less privileged backgrounds.

"Social mobility is one of the biggest challenges facing our country today," he said. "It is not just the poorest in society who are losing out. Whole communities and parts of Britain are being left behind economically and hollowed out socially."

Read more: More work, less pay — Is the UK's low-wage economy working?

The Observer cited Milburn as warning May that a failure to deal with the inequalities that fueled the vote to leave the EU would lead to even more political extremes.

"In America for 30 years real average earnings have remained flat," he said. "Now here the chancellor [finance minister] 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."

Brexit to hit economy

Britain's economic growth is being hindered by high levels of private and public debt, and the possibility of weaker links with the rest of the EU is likely to further inhibit the country's prospects.

The Resolution Foundation think tank recently warned that the UK is on course for the longest period of falling living standards since records began in the 1950s.

The social mobility commission itself has previously described a "striking geographical divide" in social mobility, where London and Southeast England continues to advance economically while other parts of the country remain in the doldrums.

Sunday's resignations couldn't come at a worse time for May, whose administration was left severely weakened when she failed to secure a parliamentary majority in a snap election in June. Before Christmas, she faces crunch talks with her EU counterparts over Britain's future relationship with the bloc.

Read more: Brexit — EU and UK 'close to financial agreement'

Meanwhile, an opinion poll published for the Mail On Sunday put May's ruling Conservatives at 37 percent, with Labour at 45 percent. The survey by pollster Survation gives opposition leader Jeremy Corbyn's party its biggest lead in four years.