The Unite boss, Len McCluskey, has accused Labour’s deputy leader, Tom Watson, of trying to turn members against Jeremy Corbyn over the leadership’s refusal to fully back a second referendum.

Tensions over the party’s second referendum policy broke out into the open on Sunday night as it braces for difficult European election results.

McCluskey suggested Watson was part of an anti-Corbyn plot after the deputy leader said Labour’s approach to a public vote was “mealy-mouthed” and directly responsible for the party losing ground to the Liberal Democrats and Greens in the European polls.

Watson won backing from one of Corbyn’s close allies, the shadow attorney general, Shami Chakrabarti, who said it was now “past midnight” and time to support a second referendum as a way of breaking the deadlock over Brexit.

McCluskey, another ally of Corbyn and general secretary of Labour’s biggest trade union donor, said Watson was acting like an ineffective Machiavelli over the issue of Brexit.

He told the BBC’s Pienaar’s Politics: “Tom Watson’s already out, surprise surprise, trying to take on the role of Prince Machiavelli, but I’ve got news for Tom. Machiavelli was effective. He’s a poor imitation of that. If he’s trying to turn Labour members against Corbyn and in his favour, then he’s going to lose disastrously.

“And there will be others in the coming days who try and do the same. Now is the time to hold your nerve, because a general election, which is the only thing that will resolve this situation, is closer now than anything.”

McCluskey also laid into some of the leading campaigners for a second referendum, including Tony Blair and former Labour spin doctors Peter Mandelson, Alastair Campbell and Tom Baldwin, claiming they were “individuals who have actually indicated they’d sooner have a Tory government than a Corbyn government, so take no notice of these phoneys and stick with Corbyn”.

The public row is an indication of serious disagreements within Labour behind the scenes over the issue of a second referendum, with Corbyn coming under huge pressure from some of his closest supporters to pivot toward more unequivocal support for one.

One Corbyn ally who favours a second referendum said he believed the “tide is turning in the leader’s office” because of the strength of feeling of members which he had seen in his own Islington constituency. He said, however, that McCluskey and several senior party advisers were still proving an obstacle to the policy changing.

Some of Corbyn’s defenders believe Watson and others are trying to use the issue of a second referendum to drive a wedge between him and the party’s membership, while gearing up to challenge him for the leadership before a general election that could come as soon as this year.

The shadow chancellor, John McDonnell, hinted that the party’s policy could move further towards a second referendum if a new Conservative leader takes the country closer to a no-deal Brexit.

“There is real threat now of an extremist Brexiteer becoming the leader of the Conservative party and taking us over the cliff edge of a no deal,” he told Sky’s Sophy Ridge on Sunday, saying Labour was seeking to work with other opposition parties. “We have got to move forward now, bring people together and block a no deal, and if that means going back to the people, so be it.”

He defended Labour’s position so far, saying it was right not to ignore the leave result of the 2016 referendum, but he acknowledged: “I think we most probably will get a good kicking in the election results tonight. We’ll see. We’re braced for that. But we had to do the responsible thing … It was a hard road to follow. But someone had to be there and say: ‘Can we bring the country back together again?’”

Before the European results were due to come in on Sunday night, Watson delivered his fullest critique yet of Labour’s lack of full support for a second referendum in an article for the Observer.

Watson wrote: “Our performance is a direct result of our mealy-mouthed backing for a public vote on Brexit when it is being demanded loud and clear by the overwhelming majority of our members and voters.

“Polls show Labour has been losing up to four times more voters to parties giving full backing to a people’s vote than to Farage. And those same polls show we would have beaten him by a country mile if we had unambiguously backed a public vote on any form of Brexit.

“Once results are in, we must channel our frustration into winning those voters back. Never again can Labour policy on the most crucial issue of our generation be on the wrong side of its members and voters.”

Watson was backed by Chakrabarti, who said it had been right to say the democratic result of the EU referendum should be carried out but a second one was needed to break the deadlock.

She told BBC One’s The Andrew Marr Show: “I was a passionate remainer but I also am a democrat and wanted to listen to the 52%. However, a confirmatory vote or a second referendum now we are in the future is a way of breaking the deadlock in our country. It is not a means of stealing Brexit from those who voted for it. It has been part of our policy since party conference last autumn. It is past midnight. So that means of breaking the deadlock is more and more important by the day.”

Chakrabarti also said it would be extremely important to stop a no-deal Brexit by any means possible, as several of the leading Conservative leadership candidates are pledging to leave the EU at the end of October, whatever happens.