The two Jeremy Corbyn allies clashed during a meeting on Tuesday, after union chiefs unanimously backed a general election campaign pledge to strike a Brexit deal with Brussels and then hold a second referendum.
The row follows months of open warfare between leading Labour figures over whether the party should take a more pro-Remain stance.
In a bid to reassure working-class Labour Leave supporters, the unions agreed the referendum ballot paper should have a credible Brexit option as well as the option to stay in the EU.
But they did not recommend calls, made by McDonnell and others, for the party to enthusiastically campaign for Remain.
In a Labour-union ‘contact meeting’, sources say McCluskey warned McDonnell, who has been piling pressure on Corbyn to back Remain in any second referendum “sooner rather than later”, that he must “toe the line”.
A union source said: “Len said something along the lines of ‘you know I think the world of you but you’re going to have to toe the line’.
“And that was the end of it - no shouting or response from John.”
Another union source added: “They have never had a good relationship anyway - John McDonnell always supported small unions and campaigns that irritated Unite before he was shadow chancellor.”
Yet another union insider claimed McCluskey made clear in the meeting it had been a mistake for McDonnell to go public on the media to give his backing for a Remain campaign, and suggested he should instead “get behind the leader”. “McDonnell looked absolutely furious,” they added.
But a spokesman for McDonnell said it was “rubbish” to suggest the Unite boss had criticised the shadow chancellor. “They had a great meeting and a constructive consultation,” he said.
Another Labour source denied the pair appeared to be at loggerheads, saying “there was no hostility at all” at the meeting.
One insider said that the unions’ priority was that the party should not turn the election into a referendum campaign itself and that it was too soon for any shadow cabinet ministers to say which side the party would back.
It comes after chiefs of Labour’s affiliated unions, who command a huge number of delegate votes at Labour conference, agreed to back Corbyn’s position that the party should go into a snap general election pledging to strike a deal with Brussels.
A Labour government would then put the deal, negotiated by Corbyn and shadow Brexit secretary Keir Starmer, to the public alongside the option of Remain as part of a second referendum.
The Trade Union and Labour Party Liaison Organisation (TULO), which has previously been riven with disagreement over Brexit unanimously backed the stance.
It is said union chiefs were persuaded that pushing for a “Labour deal” gave Corbyn ammunition to call the Lib Dems’ new policy to revoke Article 50 “undemocratic”.
Jo Swinson’s party is riding high in the polls as she attempts to position the Lib Dems as the biggest pro-Remain force in British politics.
If agreed as party policy at Labour conference later this month, however, the new position could bar anyone in the party from campaigning for Remain at the next general election.
While Corbyn could switch position, silencing Remainers could put him on a collision course with a number of pro-EU shadow ministers, including deputy leader Tom Watson and shadow foreign secretary Emily Thornberry.
Remain MPs and members have been pushing Corbyn to confirm Labour would campaign for Remain in any second referendum, but he has refused, thought to be fearing the party could lose votes in pro-Leave constituencies.
Watson broke ranks on Tuesday morning to say that Labour should push for a second referendum on Brexit before agreeing to a general election, which Prime Minister Boris Johnson has twice asked for and had denied by MPs.
But HuffPost UK understands Labour’s Brexit stance at the next election is not yet nailed down and reports Corbyn could offer his frontbench freedom to campaign as they choose in a second referendum were not confirmed.
″[Trade unions] don’t decide our policy - conference does,” said one Labour MP. “But the unions have 50% of the conference vote if they all vote the same way. I suspect there will be a couple more twists and turns before we are crystal clear where we stand, but the direction of travel is clear.”
HuffPost UK has contacted Unite for comment.
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