Labour will only back a fresh Brexit referendum “in extremis” and is determined to “get a deal done”, John McDonnell says.

The shadow chancellor cooled hopes that Jeremy Corbyn is moving towards backing another public vote, stating it was still “not the best option”.

“Let’s get a deal done – that’s the most important thing for me,” Mr McDonnell told the BBC’s Andrew Marr Show.

Insisting Labour would continue to push its softer Brexit plan – despite Theresa May rejecting it – he added: “You would only go back to the people in extremis if can’t get a deal agreed through parliament.

“Or if any deal, you thought, wasn’t going to protect jobs and the economy you would have go back to the people – and I think that’s right.”

At least five Labour MPs have threatened to quit the party, protesting that Mr Corbyn is failing to abide by a conference agreement to back a Final Say referendum if it failed to secure a general election.

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Mr McDonnell rejected that charge, insisting Labour was “keeping a referendum on the table”, but he added: “I’m not giving up on a general election.”

He did agree to “look at” a likely amendment, put forward by Labour backbenchers Peter Kyle and Phil Wilson, that would approve Ms May’s deal – provided it was confirmed by the public.

“I met Peter and Phil last week and what they’re saying is, if parliament does agree some form of deal, why not have a confirmation referendum after that?” he said.

“We’ll look at that in the debate over the next week.”

The comments come after delegates who wrote Labour’s agreed Brexit policy, last September, accused the party’s leader of betraying it.

A letter, seen by The Independent, has been sent by 23 constituency Labour party delegates who took part in a six-hour compositing meeting at the annual conference in Liverpool.

In a stinging rebuke, they remind Mr Corbyn that he promised “policy will be made by Labour members, not the leader”, and go on to say: “The complete opposite now appears to be happening.”

On the Marr programme, Mr McDonnell insisted Labour’s Brexit plan – which includes a customs union and alignment with the single market – “will come back”, despite Tory rejection.

And he warned any Labour splitters that a threatened new centrist party risked a repeat of the SDP formation in the 1980s, which “installed Thatcher”.

“That is the last thing I believe people who have been mentioned around this split would want,” Mr McDonnell said.

For more details about the Put It To The People march – and to sign up – please visit https://www.peoples-vote.uk/march