Britain's opposition Labour leader, Jeremy Corbyn, continues to rule out stepping down, despite the resignation of 10 senior members and a widespread loss of support in the party.

Mr Corbyn said on Sunday he regretted the resignations of several members of his senior team in the wake of Britain's vote in favour of leaving the European Union, but he did not plan to resign.

Ten members of Britain's Labour Party resigned hours after Mr Corbyn sacked a key member of his shadow cabinet.

"I regret there have been resignations today from my shadow cabinet," he 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.

"Those who want to change Labour's leadership will have to stand in a democratic election, in which I will be a candidate."

Twelve members of Corbyn's team withdrew their support for him on Sunday, with many criticising his contribution to the referendum campaign and saying they doubted his ability to lead the party to victory in the next election.

Pressure began mounting on Mr Corbyn from within the Labour Party after Britain voted in favour of leaving the EU in last week's referendum.

Some Labour politicians said he did not campaign hard enough in support of EU membership, and failed to convince millions of voters in the party's heartlands to back "Remain".

Hours after the vote in favour of leaving the EU, which triggered financial and political turmoil across the globe, two MPs submitted a motion of no confidence in Mr Corbyn while others have called for his resignation.

British Prime Minister David Cameron, who also backed staying in the European Union, announced he would resign shortly after the referendum result.

Former Blair advisor says people feeling buyer's remorse

Meanwhile, Alastair Campbell, former director of communications for former British prime minister Tony Blair, described the decision to leave the EU as "catastrophically stupid".

"I think the world is looking on and thinking, 'didn't you used to be a serious country?'" he told ABC News Breakfast this morning.

Sorry, this video has expired Alastair Campbell labels Brexit "catastrophically stupid"

"And I also think there's a lot of buyer's remorse going on. It makes you weep, but I was just on the way here earlier, bumping into a woman who stopped me and said she felt really bad because she voted Leave.

"I said, 'Why did you do that then?' She said, 'I didn't realise if you voted Leave it meant you had to leave'.

"We've got real problems in Europe at the moment with the rise of the far right in Germany, France, some of the other European countries, and this has just given them a great shot in the arm," Mr Campbell continued.

"Of all the world leaders, there are only three foreign policy voices, apart from Le Pen, who really come out and welcome this.

"Vladimir Putin, who is sitting in the Kremlin laughing his head off, he's managed to see the European Union destabilised without him lifting a finger."

ABC/wires