A prominent Conservative critic of Boris Johnson has said she would support a new Brexit referendum because “irresponsible” rightwingers in her party had killed off the Chequers plan.

The Cambridgeshire South MP, Heidi Allen, said she would now back a second public vote on leaving the EU because of the threat to jobs and businesses in her constituency and the rest of the country from crashing out without a deal.

It came as the Conservative party gathers in Birmingham before the start of its annual conference on Sunday, with Johnson at the centre of a huge row over criticism of Theresa May’s negotiations with Brussels.

Allen told BBC Radio 4’s Today programme she would still support in principle an “11th hour” deal hammered out by the prime minister, but many in the party, especially on the right, would not.

Describing them as “fiscally and economically irresponsible”, she said: “They have behaved unacceptably through this and have completely tied her hands.

“It is they who have made Chequers dead and that being the case – they have made their position totally clear – then I think that it is the end of the road, which is very disappointing and for me leaves us with no alternative other than asking, should we come to that and no deal ... then we need to go back to the public to decide what they want us to do next.”

Allen’s comments came as the former prime minister John Major made the case for another vote and described attacks made by some Tory MPs over May’s leadership as “completely unacceptable”.

Speaking at an event in South Shields alongside the former Labour foreign secretary David Miliband, Major said: “I do not think routine attacks on the PM in the most lurid fashion is either the spirit of politics that one would wish to see, or is it in the interest of the negotiating posture of the United Kingdom.

“The threats that come in her direction of a leadership election unless she delivers a certain sort of Brexit … [went] far beyond anything that I would think was remotely acceptable in behaviour towards any prime minister.”