Exiled Tory MPs kicked out of the party by Boris Johnson are ready to deliver a fresh Brexit referendum if, as expected, his deal is defeated on Saturday, supporters of a public vote believe.

The prime minister’s agreement was signed off in Brussels today, but opposition from the DUP means it looks set to fall in the Commons.

Supporters of a Final Say vote are confident they now have the numbers, believing up to 15 of the sacked Conservatives will join them – but only, crucially, after the deal has gone down.

For that reason, the crucial vote is unlikely to be staged on Saturday. Instead, it will be held back until after Mr Johnson’s deal has been defeated – and staged early next week, as the only solution to the new crisis created.

One former Tory, now sitting as an Independent, told The Independent: “Most of our group will back the deal but, if we wait until after it goes down, up to 15 will switch sides, plus 10-12 Conservatives with the whip.

“That would mean a majority for a referendum on the deal, but it’s vital to get the sequence right and not to move too soon.”

Philip Hammond, the former chancellor, Amber Rudd, the former home secretary, David Gauke, the former justice secretary, and former health spokesman Stephen Hammond are among ex-Tories who have left open the option of backing a referendum.

A Commons majority for a referendum became dramatically more likely after Mr Johnson took the enormous gamble of signing a deal in Brussels without DUP support – something No 10 had insisted he would never do.

Asked if Mr Johnson would win the vote, one government source replied: “I am not getting into the hubris of saying ‘we think we have got the numbers’.” Privately, Downing Street fears losing by around 20 votes.

Earlier, Labour suddenly announced it was ready to allow Mr Johnson’s deal to pass, if it is subject to a referendum, after Jeremy Corbyn was persuaded to make the leap.

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Jenny Chapman, Labour’s Brexit spokeswoman, put the chances of a successful vote for a referendum at “50-50”, admitting many of the party’s MPs were still “thinking hard” whether to back it.

“We have to respond to events as they occur and be as pragmatic as we can,” she said, explaining the shift from only backing a referendum on a “credible” deal.

Labour whips believe they can whittle down the number of its MPs voting against a referendum to under 20, down from more than 30 opponents.

Margaret Beckett, the Labour co-leader of the People’s Vote political committee, hailed the switch, saying: “Labour’s decision to back a People’s Vote on any Brexit proposal is a game changer.”

The number of Labour MPs backing Mr Johnson’s deal is expected to be “in single figures”, after he weakened Theresa May’s commitments to maintaining workers’ rights and environmental and safety protections.

The clearest mechanism to secure a Final Say referendum is to attach it to an agreed deal – as proposed by the Labour backbenchers Peter Kyle and Phil Wilson.

Mr Kyle said he was “raring to go”, but added: “I’m not saying if we are going to push it on Saturday or not.” He added: “The next 12 hours, the next 24 hours will be decisive.”

A decision not to stage a referendum showdown on Saturday could be a disappointment to hundreds of thousands of people who will be outside parliament as the debate takes place, on The Independent’s Let Us Be Heard rally.

Speaking in Brussels, the prime minister was bullish, saying: “I am very confident that, when my colleagues in parliament study this agreement, that they will want to vote for it on Saturday.”

But, hours earlier, the DUP appeared to torpedo his chances of success, accusing Mr Johnson of threatening the Union and the “professed sanctity” of the Good Friday Agreement.

The Tories’ Northern Ireland allies said they would vote against it because it created a customs border in the Irish Sea, with no power for Unionists in the Stormont assembly to block it.

“These proposals are not, in our view, beneficial to the economic wellbeing of Northern Ireland and they undermine the integrity of the Union,” the DUP statement said.

Steve Baker, the chairman of the hardline European Research Group of Conservative backbenchers, said he was still undecided.

The government had hoped as few as three or four Tory Brexiteers would vote against – but that total could double without the DUP on board.

Earlier, MPs saw off a government attempt to frame Saturday’s showdown as a “deal vs no deal” choice – by winning the right for multiple amendments, by just 12 votes.