Theresa May has called the leaders of Britain’s biggest unions for the first time since becoming prime minister in a desperate bid to find backing for her Brexit deal.

The calls to Unite leader Len McCluskey and the GMB’s Tim Roache – whose unions are Jeremy Corbyn’s biggest financial backers – mark just how far she is being forced to go in the hope of finding support for the deal expected to be rejected by MPs next week.

She was scorned by second referendum-backing Mr Roache, who joked after his call that he was “glad the prime minister finally picked up the phone”.

The unprecedented move came as she also sought to convince Labour MPs to back her by promising new commitments to maintain workers’ rights in line with EU standards after Brexit.

But expectations that she is heading for a heavy defeat on Tuesday simply grew further, with some estimates suggesting that opposition has actually grown since she delayed the vote on her deal in December.

Capitalising on the deep Tory divisions, Mr Corbyn instead invited Conservative MPs to back a motion of no confidence in the government which he is promising to table if Ms May’s plans are defeated.

Downing Street confirmed the calls to Mr Roache, whose union has 620,000 members, and Mr McCluskey, representing more than 1.4 million, and admitted it was the first time she had spoken to either of them since her arrival at No 10.

The Independent understands the prime minister also attempted to call Dave Prentis, leader of Unison which also has some 1.4 million members, but could not get through because Mr Prentis was travelling.

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The prime minister’s approach is all the more surprising because of her previous lack of engagement, with the TUC’s Frances O’Grady revealing last year that she had only met the PM once since she came to power.

Mr Roache, whose union donated almost £1m to Mr Corbyn’s Labour party in 2018, said: “After nearly three years I’m glad the prime minister finally picked up the phone.

“As you would expect, I was very clear about GMB’s position – the [Brexit] deal on the table isn’t good enough and non-binding assurances on workers’ rights won’t cut it.

“If the deal genuinely did the job for GMB members, our union would support it, but it doesn’t. It’s clear more time is required, we need to extend Article 50 and ultimately give the final say on Brexit to the public.”

The Independent has campaigned for a fresh referendum through its Final Say campaign, with more than 1.1 million people signing its petition.

But while the GMB has taken a tougher line against Brexit, Unite boss Mr McCluskey has previously warned of the consequences of attempting to hinder the UK’s departure. Unite chose to make no comment last night.

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Downing Street reported that Ms May had also talked to the CBI president John Allan and said that all of the conversations had been “constructive” and that there would be more in the coming days.

Asked if the move to call unions was desperate, her spokeswoman said: “It’s part of her ongoing engagement with leaders from across the United Kingdom.”

Earlier in the day Ms May signalled the government would “consider very seriously” a plan from Labour MPs to safeguard workers’ rights in her Brexit proposals, as part of her drive to woo the party’s Brexiteers.

An amendment tabled by Labour MP John Mann, which has the backing of his colleagues Gareth Snell, Caroline Flint and Lisa Nandy, would keep EU rules on pay and conditions, health and safety issues and environmental standards.

Mr Mann called the move part of a process, suggesting it would not immediately mean Labour MPs swinging behind Ms May’s plan.

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Ms Nandy also said its adoption would not be enough to persuade her to vote with Ms May, telling BBC Radio 4’s World at One: “The amendment that we’ve tabled, even though it represents progress, isn’t sufficient to give me or many other Labour MPs confidence that this will lead to the sort of close relationship economically with the EU that we need to protect jobs in our constituencies.”

She added: “I’ve been saying for five months now that I would be prepared to vote for the withdrawal agreement, but Theresa May needs to get in touch with Labour on our front benches and back benches, and start having this dialogue about what we need to have the confidence to vote for it. Until now, she’s only been prepared to talk to her party – particularly, the right of her party.”

Mr Corbyn was also reaching out beyond his own benches as the crucial vote approached, urging Conservatives to back a no-confidence motion in their own government to end the Brexit impasse.

The Labour leader appealed to rival parties to unite behind a bid to tear down the current administration and force a general election, admitting his party would need the support of Tory rebels to win.

He said in a speech in Wakefield: “I say to Theresa May – if you are so confident in your deal then call that election and let the people decide.

“If not, Labour will table a motion of no confidence in the government at the moment we judge it to have the best chance of success.