UK Labour leader Jeremy Corbyn has lost a confidence vote within his opposition party, following Britain's referendum to leave the European Union.

Labour members of parliament voted 172 to 40 on Tuesday against Corbyn, only two days after key members of his shadow cabinet announced their resignation.

The vote is non-binding and Corbyn said he would not resign, in a statement issued shortly after the vote.

"I was democratically elected leader of our party for a new kind of politics by 60 percent of Labour members and supporters, and I will not betray them by resigning," he said.

"Today's vote by MPs has no constitutional legitimacy."

Corbyn said he still has support in the party's rank and file.

He 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 following the vote on the Brexit, or British exit, Corbyn would fail to inspire voters towards the Labour Party - the main opposition to the ruling Conservative leadership.

Corbyn, a veteran left-winger, was elected to lead the Labour party in September 2015 on an anti-austerity ticket and the promise of renationalising the railway and major utilities.

He also promised to scrap Britain's nuclear weapons if elected prime minister.