Labour’s party chairman has reignited infighting over a fresh Brexit referendum, accusing its supporters of using the misleading term “confirmatory ballot” to confuse voters.

Ian Lavery, a key ally of Jeremy Corbyn, said some of his colleagues had realised the phrase “people’s vote” had run into the problem that “the people have already voted”.

“It’s fair to say that the terminology has changed,” Mr Lavery told The Independent, adding: “I’m not sure where the term confirmatory ballot has come from.

“I’m not saying it is trying to hoodwink people, but it is trying to appease people, trying to flower it, trying to be something it isn’t. It’s a second referendum.”

Mr Lavery is a stanch opponent of throwing Brexit back to the voters – offering to quit, last month, for defying the party whip to back another referendum in an “indicative vote”.

He described the idea of Labour giving its full-throated support to the policy as “self-harm”, because it would be seen as defying the 2016 referendum result.

And he added: “We have never – at the NEC [National Executive Committee], the shadow cabinet – we have never ever discussed the term confirmatory ballot.”

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It would see Labour agree to allow Theresa May’s deal to pass, provided it was put to the public to agree withdrawal should go ahead – or choose to Remain instead.

Both MPs hit out at Mr Lavery, Mr Kyle saying: “A confirmatory ballot didn’t confuse the people of Northern Ireland when they voted to confirm the Good Friday Agreement. It didn’t confuse voters in 2012, when they rejected electoral reform in a UK-wide confirmatory ballot.

“It certainly isn’t a good look for Jeremy Corbyn’s Labour Party to suggest the public are too stupid to answer the question ‘is this deal good enough for you and your family?’.”

Mr Wilson said the chairman appeared unaware that Labour had agreed use of the term for last month’s indicative votes, saying: “It’s party policy that it should be called a confirmatory ballot.

“Whatever the deal, it will ask the people, three years after the referendum, whether they want to confirm that deal and go ahead with it.”

Other referendum supporters favour the term “Final Say”, the campaign launched by The Independent which has attracted the support of more than 1.2 million people who signed our petition.

Mr Lavery also warned supporters that the government would be in charge of the process and accused supporters of dodging the crucial issue of the question to be asked.

“The big question with regard to that is ‘What would be on the ballot paper?’,” he said.

“Would it be Theresa May’s deal, would it be no deal, would it be Remain? People aren’t prepared to answer what would be on that ballot paper.

“This is down to whether the government will agree to have a second referendum and whether or not the Labour Party should be putting itself through what I describe as self-harm. Is this wise?”

Mr Lavery also accused the Parliamentary Labour Party (PLP) of being “very unfair” to Mr Corbyn, after he was sharply criticised at recent meetings.

“There has been a lack of respect for the fact that Jeremy is the leader of our party and I would urge MPs and peers to recognise that,” he said.

“The behaviour we see at the PLP has been quite different to what we have experienced under different leaders.”