Labour has taken a big step towards full backing for an EU referendum after the country’s biggest trade unions agreed the party should demand a public vote on Brexit – regardless of who is in power.

The position agreed by unions including Len McCluskey’s Unite states Labour should push for a referendum regardless of the Brexit plans put forward by the Tories. The unions decided Labour should also campaign to stay in the EU.

They also said that, in the event of a general election won by Labour, the party should still offer the public a Final Say. However, it would be up to Labour to decide whether it campaigned to remain in the EU or supported leaving with its own deal.

There was no immediate official response from the party or leader Jeremy Corbyn.

But a senior source said: “Jeremy has been working to unite the party and the wider Labour movement around a common position. It is pleasing to see the unions come together around the common position.”

It is expected that the announcement will be discussed by Labour’s ruling National Executive Committee and shadow cabinet in separate meetings on Tuesday, though it is not known how soon an official change in policy could be agreed.

It represents a significant advance for Remain-backing forces within the Labour movement after months of half-hearted policy commitments.

But the party’s deputy leader Tom Watson, who has been pressing Mr Corbyn to throw Labour behind a full-blooded Remain campaign, made clear he did not believe the union decision went far enough for the majority of supporters and activists who want to stay in the EU.

“Remain is who we are,” said Mr Watson. “Our values are Remain, our hearts are Remain.

“Today is a step in the right direction, but our members and supporters are clear that any kind of Brexit gives us less than we have and Labour should not support it.”

The unions said they support giving the public the option on the ballot paper of either accepting the Tory outcome or remaining in the EU. In this scenario, they agreed Labour should campaign to remain in the EU.

But if a general election is called before Brexit is delivered, the unions said Labour’s manifesto should promise to negotiate a softer “jobs-first” Brexit with the EU, which would respect the Leave outcome of the 2016 referendum.

Any deal achieved by Labour should then be put to a Final Say vote, with Remain on the ballot paper. But the decision on which side the party should support in this referendum would “depend on the deal negotiated”.

The breakthrough comes amid growing pressure on Mr Corbyn to clarify Labour’s ambiguous Brexit stance, which critics blame for driving Remain-backing voters into the arms of Liberal Democrats and Greens in European elections – when the party took just 14 per cent of the vote.

Corbyn has been asked time and again to announce full-blooded Brexit policies (Reuters)

Unite boss Len McCluskey has been accused of blocking a move towards full-throated support for a referendum and a Remain campaign.

But union sources said Mr McCluskey was “comfortable” with the agreement thrashed out at today’s meeting, which they characterised as “good-natured and constructive”.

One source said the meeting, attended by a range of Labour-backing unions but without any party officials in attendance, had shown “a real collective desire to come to a unified position”.

The Labour chair of the Exiting the EU Committee, Hilary Benn, hailed the union move as “a very significant development” which should lead to “swift” change to the party’s official policy.

Mr Benn said: “Jeremy himself has said he wanted to consult with the unions and others.

“Now it appears that agreement has been reached in the discussion with trade unions today, I hope the shadow cabinet will be able very swiftly to come out and say Labour is unequivocally supporting a second referendum with Remain on the ballot paper – and crucially, that the Labour Party is supporting Remain.”

A Conservative spokesperson said: “This once again makes clear that Labour have no interest in delivering on the referendum result.

“Labour promised to respect the Brexit vote, but re-running the referendum and backing Remain would be an attempt to frustrate Brexit and ignore the democratic mandate to deliver it.”

And Liberal Democrat Brexit spokesperson Tom Brake dismissed the union agreement as a “fudge”.

“The unions seem to have moved to a position to support Liberal Democrat policy to stop a Tory Brexit,” said Mr Brake. “However, a Labour Brexit would be no better. Labour must rule out their Brexit-supporting leader negotiating their own Brexit deal.