Conservative supporters of a fresh EU referendum have officially launched a new campaign group, as one MP admitted the party had created the current “mess” over Brexit while another declared Theresa May’s deal “dead”.

At the first major event of the new group – Right to Vote – it was claimed several cabinet ministers and junior ministers had “intellectually” arrived at the second referendum argument and were considering whether to publicly back the idea.

Those present included MPs Heidi Allen, Sarah Wollaston, Anna Soubry, Dominic Grieve, Justine Greening, Phillip Lee and Sam Gyimah.

It was claimed that one backbencher was not present at the news conference after receiving a “credible death threat”.

Launching the push for a Final Say referendum, Mr Lee said the prime minister’s Brexit deal – defeated by a historic margin on Tuesday – was “dead”, adding: “There is no use in doctors like me or Sarah trying to resuscitate it – it is beyond recovery.”

He continued: “The prime minister spent two and a half years trying to reach an agreement on the UK’s exit from the European Union that will command support and she has failed.

“It is no good trying to tweak this agreement in a few places and trying again. And it’s no good telling the public they can’t have a Final Say while insisting it is fine for MPs to be asked to vote again and again until the government gets the answer it wants.”

Ms Allen, the Conservative MP for South Cambridgeshire, claimed, however, that is was “especially hard” for some Tories to fully back the campaign for a fresh vote.

“You know what, I’m going to say it, we created this mess,” she said.

Ms Allen added: “Quite a few of us are saying, ‘well you know we need to exhaust all the options first. We need to go around that Norway loop, again … my association are going to deselect me’, but to hell with your associations, it’s your voters you should be worried about.”

Also speaking at the launch event, Mr Gyimah, the former universities minister who resigned to vote against Ms May’s Brexit deal, poured cold water on the current cross-party talks initiated by Ms May in the last 24 hours.

He said Brexit had until now been approached as a “Conservative Party project, rather than a national project” making any cross party talks difficult, as he described the referendum route as the “life raft”.

Asked by The Independent whether they could back a vote of no confidence in the government – brought by Jeremy Corbyn – if the prime minister was to oversee a no-deal Brexit, Mr Lee replied: “What I would say on this is that on both sides passions run high, and people are very exercised about Brexit, about no deal.

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“I think some people are feeling like well I’m going to do everything about that and that’s why it’s another justification for going down this path [referendum]. Nobody wants do what you’re implying, nobody wants to cross the floor, nobody wants to do that.

“I think that No 10 needs to recognise that passions are equally strong on the no Brexit side as on the Brexit side. I think it’s just been downplayed because the other side have been getting a bit more aggressive in inverted commas in terms of the way they go about things.

“I don’t think it would be a good idea for the government to go down ... to push us up against the wall at the end of March.”