Britain's opposition leader Jeremy Corbyn is facing a crisis within his Labour Party following the EU referendum, having sacked one shadow cabinet minister for attempting a coup, and as more than a dozen other members resigned, citing ineffective leadership.

But, a defiant Corbyn said he will stand in any new Labour leadership election and "reshape" the shadow cabinet within a day.

"I regret there have been resignations today from my shadow cabinet," the Labour leader said in a statement late on Sunday. "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.

Labour resignations so far: - Lord Falconer, shadow justice secretary - Anna Turley, shadow minister for civil society - Chris Bryant, shadow Commons minister - Karl Turner - shadow attorney general - Chris Bryant, shadow leader of the House of Commons - Heidi Alexander, shadow health secretary - Lucy Powell, shadow education secretary - Vernon Coaker, shadow Northern Ireland secretary - Ian Murray, shadow Scottish secretary and Labour's only MP in Scotland - Kerry McCarthy, shadow environment secretary - Seema Malhotra, shadow chief secretary to the Treasury - Lillian Greenwood, shadow transport secretary - Yvonne Fovargue, junior shadow consumer minister - Steve Reed, shadow minister for local government - Alex Cunningham, junior shadow minister for environment - Roberta Blackman-Woods, junior shadow housing minister - Wayne David, junior shadow minister in justice, Scotland and Cabinet Office - Gloria de Piero, shadow minister for young people and voter registration - Diana Johnson, shadow foreign minister - Toby Perkins, shadow armed forces minister

"Over the next 24 hours I will reshape my shadow cabinet and announce a new leadership team to take forward Labour's campaign for a fairer Britain."

In the early hours of Sunday, Corbyn sacked shadow foreign secretary Hilary Benn as deep divisions emerged in the Labour Party following the UK's vote to leave the European Union.

Corbyn, facing pressure to step aside after Thursday's referendum, dismissed Benn after reports that he was preparing to lead a coup against the Labour leader.

Hours later, Heidi Alexander, the shadow health secretary, resigned. Soon after, Gloria de Piero, the shadow minister for young people, also quit, among many others. Shadow Commons leader Chris Bryant and Anna Turley, shadow minister for civil society, were among those who resigned a day later, on Monday.

In a letter posted to Corbyn, published on her Twitter page, Turley said: "[I] do not believe the Labour Party under your leadership is, or ever will be, in good enough shape to go to the public in an election and ask to serve them in government."

Corbyn has been criticised for not campaigning hard enough in support of EU membership, and had failed to convince millions of voters in the party's heartlands to back "Remain".

Many fear that should another general election be held in the wake of the Brexit, or British exit, vote, Corbyn would fail to inspire voters towards the Labour Party - the main opposition to the ruling Conservative leadership.

In a statement, Benn said he was sacked after telling Corbyn in a phone call that he had lost confidence in his leadership.

"It has now become clear that there is widespread concern among Labour MPs and in the shadow cabinet about Jeremy Corbyn's leadership of our party. In particular, there is no confidence in our ability to win the next general election, which may come sooner than expected, if Jeremy continues as leader," Benn said.

Benn, the son of former Labour politician Tony Benn, also publicly disagreed with Corbyn in September over air strikes on Syria.

Soon after the 52 to 48 percent vote in favour of Brexit, which triggered the resignation of Prime Minister David Cameron, two Labour MPs - Margaret Hodge and Ann Coffey - submitted a motion of no confidence in Corbyn.

'Immigration debate needed'

Around one third of Labour voters are estimated to have backed a British exit from the EU on Thursday, with many of those coming from traditional working-class areas where high immigration tops the list of public concerns.

Responding to criticism from Labour colleagues that he had failed to address those concerns, Corbyn said there needed to be a national dialogue on immigration to reach a new settlement.

READ MORE: After Brexit, what happens next?

"We can't duck the issue of immigration. Clearly it was a factor," he said. "We need to start an open and honest debate."

Corbyn said the vote showed a backlash against the EU principle of free movement. But he added that if Britain wanted to retain access to the European single market - one of many issues cast into doubt by the vote - he believed it would have to accept free movement as a condition of that deal.

"If we were part of the single market in future, then clearly that would be accompanied by the continuing free movement of people," he said.