London (CNN) The leader of Britain's opposition Labour Party has vowed not to step down amid challenges to his leadership as the fallout from the UK's momentous vote to leave the European Union continues.

Eleven senior MPs resigned from Labour leader Jeremy Corbyn's shadow cabinet on Sunday, according to UK media, after shadow foreign secretary Hilary Benn was sacked by Corbyn for reportedly plotting against his leadership in the wake of Thursday's referendum.

"I regret there have been resignations today from my shadow cabinet," Corbyn said in a statement. "But I am not going to betray the trust of those who voted for me - or the millions of supporters across the country who need Labour to represent them."

Corbyn said there would be a new shadow Cabinet within 24 hours and, if there was a new vote for the Labour leadership, he would stand as a candidate.

Under Britain's parliamentary system, the shadow Cabinet is a senior group of opposition members of Parliament tasked with criticizing the government's policies; each is given a specific portfolio on which to act as spokesperson.

Plotting alleged

The turmoil began when Corbyn fired Benn on Sunday following reports that he was planning a coup against his leadership, Britain's Press Association reported.

British Labour MP Hilary Benn in London Sunday following his sacking from the shadow cabinet.

The agency quoted a Labour spokesman as saying, "Jeremy has sacked him on the grounds that he has lost confidence in him."

Benn described the events to the BBC on Sunday, saying it had become "increasingly clear that there is growing concern in the shadow Cabinet, in the parliamentary Labour Party, about (Corbyn's) leadership."

"I said to him that I no longer had confidence in his leadership. He then dismissed me from the shadow Cabinet, which is understandable, and I thanked him for having given me the opportunity to serve as shadow foreign secretary," he said.

MPs resign from shadow cabinet

Benn's sacking was followed by multiple shadow Cabinet resignations, including shadow cabinet of shadow health secretary Heidi Alexander, shadow Scottish secretary Ian Murray, shadow education secretary Lucy Powell, shadow secretary for environment, food and rural affairs Kerry McCarthy and shadow chief secretary to the treasury Seema Malhotra.

It is with regret that I confirm I have resigned from the Shadow Cabinet. Here is my resignation letter. pic.twitter.com/sUqB4Cby0R — Seema Malhotra (@SeemaMalhotra1) June 26, 2016

Shadow leader of the House of Commons Chris Bryant was the latest senior MP to resign, after telling Corbyn he had to step down.

"I urge you, because you are a decent man to do the decent thing and take the only action that can avert potential disaster by stepping down," he wrote in his resignation letter.

Malhotra wrote in a letter to Corbyn that she was proud of the opposition's past work, particularly in protecting tax breaks for working people. But it has become clear since the EU referendum that "we do not currently look like a government in waiting," she said.

"I have come to the view that under your leadership we will not be able to build bridges across the party, be the strong official opposition that the country needs or reach out to voters and build confidence in Labour, " she told Corbyn.

Alexander wrote in her resignation letter that in the wake of the referendum result, the country faced "unprecedented challenges," and she believed a change of leadership in the party was "essential."

It is with a heavy heart that I have this morning resigned from the Shadow Cabinet. pic.twitter.com/amBRk30RtR — Heidi Alexander (@heidi_mp) June 26, 2016

"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 and I believe that if we are to form the next Government, a change of leadership is essential," she wrote.

In his resignation letter, Murray wrote that the country faced a "deeply challenging time ahead" following the Leave vote, and required a "strong opposition."

UK Labour needs new leadership to take the country forward. Today I have resigned from the Shadow Cabinet. (2/2) pic.twitter.com/7eoLtF5bmC — Ian Murray (@IanMurrayMP) June 26, 2016

"I do not believe that can be achieved under your leadership," he wrote.

Powell and McCarthy also cited the challenges created by the referendum result in deciding to resign.

My letter to Jeremy Corbyn setting out some of the challenges facing us following Thursday's vote. pic.twitter.com/EBbSnOlbaF — Kerry McCarthy (@KerryMP) June 26, 2016

Another prominent Labour MP, Chuka Umunna, tweeted his support for Benn, saying it was "crazy to sack him."

He followed this with a tweet saying, "Either you look your flaws in the face and address them or you stick your head in the sand, destroy the Labour Party and the country suffers."

Corbyn has canceled a speech scheduled to take place at the Glastonbury Festival in Pilton on Sunday, his spokesman told CNN.

Pressure mounts on Corbyn

Like Conservative Prime Minister David Cameron, who announced his intention to resign Friday in the wake of the vote, the Labour Party campaigned for Britain to remain in the EU.

But Corbyn, who became leader of the Labour Party in September, has been criticized for his lackluster performance in campaigning for the "Remain" camp.

Pressure has been mounting for him to follow his rival Cameron and step down in the wake of the referendum result, which has fractured Britain's political establishment.

Corbyn's close ally and shadow Cabinet member Dianne Abbott tweeted Friday that the Labour leader's "position on Brexit was closer to the national mood than any other leader of a major party."

Jeremy Corbyn's position on 'Brexit was closer to the national mood than any other leader of a major party — Diane Abbott MP (@HackneyAbbott) June 24, 2016

Divided kingdom

The EU referendum bitterly divided the nation, with 51.9% of voters casting their ballots to leave and 48.1% voting to remain.

The result was met with shock and anger in many quarters, sent the pound and markets plunging, and has left a leadership vacuum as the country faces an uncertain future.

Speaking to British media Sunday, British Foreign Secretary Philip Hammond said that Britain losing access to the European single market following the Brexit vote would be "catastrophic."

Some "Leave" voters have expressed regret about their choice, saying they did not realize the consequences would be so great, and an online petition calling on the government to hold a second, "do-over" referendum on the issue has gathered more than 3 million signatures.

The "Leave" vote could lead to the fracturing of the United Kingdom itself.