A string of Conservative MPs have said they can no longer back Theresa May’s Brexit deal, in a sign that many could be willing to vote it down in order to hasten her departure as prime minister.

At least 23 Tories who backed the deal last time said they were unlikely to support her revised “10-point offer” this time for various reasons – from opening the door to a second referendum, to its package of measures designed to appeal to Labour MPs. And by Tuesday evening not a single backbencher who opposed the deal last time had come forward to say they would support it.

Among those to withdraw their support were leading Brexit supporters including Boris Johnson, Dominic Raab, Zac Goldsmith, Jacob Rees-Mogg and David Davis.

Johnson, a Tory leadership frontrunner, said it was “against our manifesto and I will not vote for it”.

Raab, another leading candidate, said he would swap back to opposing it, saying: “I cannot support legislation that would be the vehicle for a second referendum or customs union. Either option would frustrate rather than deliver Brexit, and break our clear manifesto promises.”

Some more centrist Conservatives also suggested they might not support it, including Rob Halfon, who had supported a Norway-style common market Brexit, the leadership hopeful Johnny Mercer, and Andrew Percy, who had led the Brexit delivery group of around 100 MPs who previously supported May’s deal.

Percy told the BBC: “I’m frustrated. I voted for this at meaningful vote one, two and three … but I really am concerned about the proposed possibility of a second referendum. People were told it was the final say on the matter for a generation and it would be implemented. I haven’t decided how I will vote yet but I find this offer of a second referendum really, really worrying.”

Halfon said opening the door to a second referendum appeared to be a “betrayal of the 2016 referendum and a betrayal of everything she has been saying since she became prime minister”.

Goldsmith said: “I cannot support this convoluted mess. That it takes us towards a rigged referendum between her deal and no Brexit is just grotesque. The PM must go.”

At a meeting of the European Research Group of pro-Brexit MPs, a source said the mood had turned definitively against May’s deal.

The draining away of Conservative support for May’s deal suggests it could be defeated by a much greater margin than last time, when it lost by 58 votes.

With the Labour frontbench still opposed to the legislation, May would need dozens of backbench opposition MPs to change their vote.

She namechecked two Labour backbenchers, Gareth Snell and Lisa Nandy, in her speech, saying she had made concessions to their demands for assurances that parliament would have a say on any final Brexit deal.

However, Nandy said she could not vote for it without further promises and Snell did not guarantee his backing either.

Neither did May’s promise of a “new workers’ rights bill to ensure UK workers enjoy rights that are every bit as good as, or better than, those provided for by EU rules” satisfy leading trade unionists.

Frances O’Grady, the general secretary of the TUC, said: “This reheated Brexit deal won’t protect people’s jobs and rights. The PM only has weeks left in the job and her likely successors are queuing up to say they’ll ditch this deal. We need a legally binding guarantee for workers’ rights, written into the treaty with the EU.”

Some MPs campaigning for a people’s vote had argued that attaching a second referendum to the deal would be a route to attracting cross-party support but the offer of a vote was not enough to satisfy them.

Peter Kyle, a Labour MP and one of the architects of the Kyle-Wilson plan, said: “The prime minister just made a whole load of promises on behalf of the next prime minister. That’s likely to be someone who has repeatedly voted against the very things she’s announcing. No thanks.

“Kyle-Wilson was offered to her as a clean, simple confirmatory public ballot on her deal. After an eye-roll, the prime minister promised a strange, complex, Commons process. This is not leadership and not good enough.”