The post-Brexit crisis enveloping British opposition Labour leader Jeremy Corbyn deepened on Sunday with reports saying up to half his shadow cabinet planned to resign after shadow foreign secretary Hilary Benn was sacked.

"It is with a heavy heart that I have this morning resigned from the shadow cabinet," shadow health secretary Heidi Alexander said on Twitter, posting a photograph of her letter to Corbyn.

Thursday's vote to withdraw from the European Union leaves Britain facing "unprecedented challenges," Alexander said in her letter.

She said the country needs an opposition "capable of developing a credible and inspiring alternative to an increasingly right-wing and backward-looking Conservative Party."

"As much as I respect you as a man of principle, I do not believe you have the capacity to shape the answers our country is demanding," Alexander told Corbyn.

Britain's two main political parties have fallen into turmoil after their leaders lost the campaign to prevent a Brexit, or British exit for the European Union. Conservative Prime Minister David Cameron offered his resignation on Friday.

Alexander's resignation followed left-winger Corbyn's sacking of Benn, a centrist who told the Labour leader he had lost confidence in him.

"In a phone call to Jeremy I told him I had lost confidence in his ability to lead the party and he dismissed me," Benn told the BBC.

"There is no confidence to win the next election if Jeremy continues as leader," Benn said.

The broadcaster said up to half of the other 28 shadow cabinet members planned to resign.

Gloria De Piero, the party's shadow minister for young people, also resigned on Sunday, the BBC and other media said.

Meanwhile, an online petition for a "vote of confidence in Jeremy Corbyn after Brexit" had some 173,000 supporters by midday Sunday.

Two other senior Labour politicians, Ann Coffey and Margaret Hodge, have proposed a vote of no confidence against Corbyn at a meeting on Tuesday, amid criticism that Corbyn's referendum campaign was too weak.

Labour lawmaker Tristram Hunt, a former shadow cabinet member, said the referendum had "exposed with terrifying clarity tensions within the Labour movement that have built up over the last decade."

Hunt called for Corbyn's resignation in a letter published on Sunday in The Observer, a sister paper of The Guardian, saying his "real crime during the campaign was a failure to insert Labour values about workers' rights and European solidarity into the debate.

"Truth be told, he was never that interested in keeping Britain in Europe and the public clocked it," Hunt said.

Writing in the same paper, another Labour lawmaker, Stephen Kinnock, said he was backing the no-confidence motion against Corbyn.

"Corbyn is a great campaigner – but we need a hard-headed negotiator," Kinnock said.

"Our leader must be held accountable for the failure of the 'Labour In For Britain' campaign, as must we all," he said.

Corbyn did not appear with Cameron at any Remain campaign events, and, like the prime minister, he did not take part in any of the television debates on the pros and cons of a Brexit.

Both leaders, like most Conservative and Labour politicians campaigning for Remain, largely avoided debate on migration until the final few weeks of campaigning, when there were already fears that the issue could lose the referendum for Remain.

The BBC said Corbyn's election in September, "at the age of 66, must count as one of the biggest upsets in British political history." He was backed by some of Britain's largest trade unions.

Most of his Labour critics are centrists in British politics. Many are known as Blairites because of their association with former Labour prime minister Tony Blair and his allies in the party.

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