Labour is poised to declare it will campaign for remain in a second referendum on any deal put to parliament by a Conservative prime minister, after trade union leaders including Unite’s Len McCluskey backed a change of policy.

The joint position agreed by the unions on Monday would not commit Labour to an explicitly pro-remain position in all circumstances: unions also agreed Labour should seek to deliver a Brexit deal if the party won an election before the UK left the EU.

That Labour deal would also be put to a public vote, but the party would not commit to campaigning for remain against its own Brexit deal, throwing into doubt what Labour would offer in any snap election manifesto.

One senior shadow cabinet source described it as a significant win for remain campaigners, despite the potential lack of clarity.

“Unions have backed a referendum on any deal this parliament and Labour campaigning for remain – that’s a big victory. What’s in a manifesto is a debate for another day,” the source said.

Barring any major intervention, the surprise consensus among trade unions including Unite, GMB, Unison, Aslef and Usdaw is likely to force any remaining sceptics to agree to the new position when the shadow cabinet meets on Tuesday.

Several shadow cabinet sources said the policy had the hallmarks of being approved by the Labour leader’s office and said it “would not be watered down” – though some shadow ministers are likely to push for an even stronger position.

Labour’s deputy leader, Tom Watson, who has regularly clashed with Jeremy Corbyn over the party’s Brexit position, tweeted: “Remain is who we are. Our values are remain, our hearts are remain. Today is a step in the right direction but members and supporters are clear that any kind of Brexit gives us less than we have now and Labour should not support it.”

Union leaders had met on Monday to agree a common position on Labour’s Brexit policy, in a meeting one source described as fractious but ultimately consensual.

The proposed policy, which will be offered to the Labour leadership as the unanimous view of the unions, will say:

Labour will campaign for a second referendum in all circumstances and will campaign for remaining in the EU against a Tory prime minister’s Brexit deal and in order to stop no deal.

Should Labour win a general election before Brexit, Labour would negotiate its own Brexit deal and then hold a referendum with remain on the ballot paper – but the party should not specify whether it would back remain in those circumstances.

A senior Labour source said Corbyn had not been present at the meeting but suggested it was a helpful outcome. “Jeremy has been working to unite the party and the wider Labour movement around a common position,” the source said.

Union sources close to the talks said they did not want the position to be presented as an out-and-out victory for remain campaigners, saying the party would still have a chance to tell leave voters it would honour the result of the 2016 referendum by negotiating a Brexit deal if in government.

“Ultimately everybody just wants this to end,” one union source said. “It would be an error to let this drag on until conference and have the battle on the conference floor. But it is right to reserve the position on a Labour-negotiated Brexit deal which could deliver the result of the 2016 referendum. It would be mad to say we would negotiate a deal and then campaign against it.”

One union source said the meeting had been lengthy but amicable and its purpose had been to find a consensus. “We are pleased and confident that everything is on the right road,” the source said.

A briefing war has erupted over the past few weeks as some shadow cabinet ministers suggested senior Corbyn aides and union figures such as McCluskey were preventing the party moving to an explicitly pro-remain position or championing the change in party policy.

On Sunday, the shadow chancellor, John McDonnell, denied claims he had been urging Corbyn to sack his two most senior aides, Karie Murphy and Seumas Milne, because they were opposed to Labour committing to backing remain in a second referendum.

Labour had already shifted its Brexit stance to propose that any Brexit deal passed by parliament should be put to the people in a second referendum, after the party suffered heavy losses to the pro-remain Liberal Democrats at the local and European elections.

Diane Abbott, the shadow home secretary, had previously said publicly she was “beginning to worry” about party policy not being sufficiently pro-remain.

Labour MPs at a private meeting of parliamentarians on Monday night expressed some caution about the new policy.

“It is not exactly the absolute clarity we were hoping for,” one MP said. “It sounds like we are reserving the right to campaign for remain against our own Brexit deal – that will just sound ludicrous to voters.”

The party came under attack for the policy from both sides of the Brexit divide as the trade union agreement emerged. The Conservatives called it “an attempt to frustrate Brexit and ignore the democratic mandate to deliver it”.

The Liberal Democrat Brexit spokesman, Tom Brake, said: “Even now, after millions of remainers have deserted them, Labour manage only a fudge.”