Britain's opposition Labour Party is sliding into turmoil in the wake of the U.K.'s vote to exit the European Union, a sign of how hard the shock decision is shaking British politics.

Two senior party members left the shadow cabinet Sunday amid a dispute over the leadership of Labour chief Jeremy Corbyn.

The vote to quit the EU was widely seen as a stinging rejection of left-wing Labour, with many traditional Labour districts voting in defiance of the party leadership's campaign to stay in the bloc.

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.

On Sunday, Corbyn fired shadow foreign secretary Hilary Benn after Benn told Corbyn he had lost confidence in his ability to lead the party.

"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's flagship breakfast show. "He's a good and decent man, but he is not a leader. And that's a problem."

Benn's dismissal was followed by the resignation of Labour health spokeswoman Heidi Alexander, who 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 departures followed claims in the Observer newspaper that Benn was plotting against Corbyn.