Keir Starmer slapped down Jeremy Corbyn’s aides as he vowed Labour would back moves to give voters the chance to reject Theresa May’s Brexit deal in a fresh referendum.

The Labour leader’s advisers are accused of watering down the party’s surprise commitment to a referendum – suggesting it would not cover putting the prime minister’s agreement on the ballot paper.

But Sir Keir, the shadow Brexit secretary, insisted “elected politicians” had decided the policy, with Mr Corbyn’s agreement, saying: “If Theresa May’s deal goes through, it is subject to the lock of a public vote.”

The cracks emerged within hours of the announcement, which has been hailed as potentially “a defining moment” in the campaign for a Final Say referendum on the Brexit outcome.

Mr Corbyn – desperate to head off further defections to the breakaway Independent Group – said he would back another public vote if, as expected, his own softer withdrawal plan is defeated this week.

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A briefing note for MPs said an amendment “could be attached to the prime minister’s deal – or a version of it – should it win a majority in the House of Commons”.

The sentence was a reference to the amendment put forward by Labour backbenchers Peter Kyle and Phil Wilson, for a confirmatory referendum.

However, on Monday night, a Labour source said the party would not support the amendment in its current form, because “we will not be voting for anything which supports May’s damaging Brexit deal”.

A second, anonymous sources briefed that Emily Thornberry, the shadow foreign secretary, “misspoke” when she said the referendum was likely to be Ms May’s deal vs Remain.

Asked if Mr Corbyn’s aides were attempting to dilute the pledge, Sir Keir said: “You have got elected politicians on your programme – you had Emily Thornberry out last night – setting out what the position is that we agreed as the Labour party.

“What I am saying is telling you what was in the written briefing, the official briefing from my office and Jeremy’s office, to Labour MPs last night

“There is no question about that – it should be between a credible Leave option and Remain.”

Sir Keir made clear that a “credible Leave option” meant Ms May’s deal, if approved – although it is still unclear if Labour will abstain to allow it to pass, subject to a referendum.

It appeared Mr Corbyn’s aides were suggesting Labour would only back a referendum on its own Brexit proposals, which are almost certain to be rejected by MPs.

Speaking on BBC Radio 4’s Today programme, Sir Keir also sought to play down suggestions that at least 25 Labour MPs would refuse to back a second referendum in a Commons vote.