The vote to quit the EU was widely seen as a stinging rejection of the left-wing Labour Party, with many traditional Labour districts voting in defiance of the party leadership's campaign to stay in the bloc.
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At least 11 members of the Labour Party's "shadow cabinet" left their posts in a direct challenge to Corbyn.
Ten resignations followed Corbyn's firing of shadow foreign secretary Hilary Benn, who told Corbyn he had lost confidence in Corbyn's ability to lead.
"There is no confidence that we will be able to win a general election as long as Jeremy remains the leader," Benn told the BBC. "He's a good and decent man, but he is not a leader. And that's a problem."
Labour health spokeswoman Heidi Alexander released a letter saying a change of leadership was needed.
"Those who will be hit hardest by the economic shock associated with the vote to leave the EU need a strong opposition, as do those communities who fear rising levels of intolerance, hatred and division," she wrote.
The perceived mishandling of the EU campaign bodes poorly for any future attempt by Labour to retake its parliamentary majority from the ruling Conservative Party, which itself is in limbo following the decision by Prime Minister David Cameron to quit in the fall.
Corbyn was elected leader in September with strong support from the left wing of the party, but he has not enjoyed similar backing from the group's legislators, some of whom are now calling for him to step down.