A fresh attempt to oust Theresa May is under way over her decision to enter into talks with Jeremy Corbyn, with leading Brexiter MPs plotting ways to force a vote showing that the majority of the party has lost confidence in her.

Sir Graham Brady, the chair of the 1922 Committee, has rebuffed calls from backbenchers for an indicative vote on May’s future, because the prime minister saw off a no-confidence vote in December last year and cannot be challenged again within 12 months.

However, backbench MPs are submitting a fresh batch of no-confidence letters to him in the hope the number will become so great that he has to act.

After meeting the prime minister on Monday, Brady said there was “no intention of proceeding” with any informal vote of confidence.

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It is understood the 1922 Committee debated the issue for almost an hour last week and was split over whether it should go ahead. Some Conservative MPs were under the impression Brady had ruled it out only “for now” and would be forced to give in to pressure to hold a vote if he received a deluge of letters.

One MP said Brady had told them he would pass on the concerns of colleagues to May herself and, of the letters, “she won’t know the names but she will know the number” who were unhappy with her. Another Conservative MP said that if Brady would not allow an indicative vote then “we will find a way around him”.

Mark Francois, the vice-chair of the hardline European Research Group, called for an indicative ballot to take place this week as he said May had lost the confidence of her MPs.

In a letter to Brady, Francois said: “If my colleagues were to demonstrate prior to Wednesday evening, in an indicative ballot say at 3pm, prior to the meeting of the 1922 Committee, that they have lost confidence in the prime minister, I believe that under those circumstances it is extremely unlikely that the European council would grant an extension and we would, therefore, leave the European Union on Friday night, as so many Tory MPs so obviously want. Our future is therefore literally in the hands of 313 Tory MPs.

“I believe May has been a failure as leader of our party, which she now threatens to destroy. Hers is a classic example of hubris – and after hubris, comes nemesis.”

Beth Rigby (@BethRigby) NEW: Mark Francois writes to Brady to request informal indicative vote of no confidence in PM on Weds 3pm b4 EUCO “I believe May has been a failure as Leader of our Party, which she now threatens to destroy. Hers is a classic example of hubris – and after hubris, comes nemesis.” pic.twitter.com/i6DCSgX3zd

Francois later told the Guardian: “When we had an official vote of confidence prior to Christmas and 117 colleagues voted against the PM, we did not know at that time that she would be getting into bed with a Marxist with the prospect of a customs union and breaching the 2017 manifesto. Had we known that, I’m sure the vote against would be far higher. Now that everything has changed, I believe it is appropriate that colleagues should be asked again.”

The Tory MP James Duddridge said: “We shouldn’t be bound by the party rules that we cannot have a vote for 12 months. If an indicative vote is good enough for the Commons, it is good enough for the internal party rules. Prior to that, Graham Brady was already collecting signatures. There were some people encouraging others to put in additional signatures.”

Andrew Bridgen, another Conservative MP who is against May’s deal, first brought up the idea a week ago, saying an “indicative vote” should be considered. “It seems to be all the rage, so why not?” he said.

May has signalled she will step down as the prime minister if her Brexit deal passes, but it still shows no sign of going through parliament.

Over the last week a supportive letter has been circulating among MPs expressing backing for May opening talks with Labour, but it is not clear how many have signed it.