Theresa May’s grip on power appears to be slipping as speculation grows at Westminster that she could face a vote of no confidence from Tory MPs exasperated at her last-minute decision to pull the meaningful vote.

While the prime minister took a whistlestop tour of European capitals on Tuesday in an effort to win fresh concessions from EU leaders, MPs were lobbying colleagues to submit letters of no confidence in her leadership to Graham Brady, the chair of the 1922 Committee of backbenchers.

Friends of Brady refused to deny reports he would meet May after her regular appearance at prime minister’s questions on Wednesday lunchtime. He would have to inform her first, before calling any no confidence vote.

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There was fevered speculation at Westminster on Tuesday night that the threshold of 48 letters – which would trigger a vote – had finally been reached.

The former environment secretary Owen Paterson, a prominent leave campaigner who has been a trenchant critic of the prime minister’s approach, made his own letter of no confidence public. He said May’s deal represented a series of “broken promises” and was the culmination of “more than two years of poor government decision-making”.

Several prominent Tories, including Boris Johnson, Sajid Javid and Amber Rudd, are known to be contemplating running if May loses a confidence vote.

Many of the most prominent May sceptics were wary of making predictions, bruised by the last time the letters failed to materialise. One Brexiter MP said he knew colleagues who had spent the day lobbying others to send in their letters. Another said: “Do I think we’re there yet tonight? I’m not sure, but I think we will be tomorrow.” Others played down the prospect of the threshold being reached.

Brady said last month that party rules made clear any vote of no confidence should take place “expeditiously”.

“The intention is clear that if it were to happen, it ought to be a test of opinion, very quickly, in order to clear the air and get it out of the way so that the party, the government at the moment, can move on,” he said.

A vote of Tory MPs could take place within days and if May lost it she would not be able to stand in the subsequent leadership contest, which could run through the Christmas recess.

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Meanwhile the EU is moving into full no-deal mode, with May’s shock decision to pull Tuesday’s vote on her Brexit deal prompting Brussels’ chief negotiator, Michel Barnier, to warn privately of a sudden escalation of risk.

May is due to hold a cabinet meeting on Wednesday afternoon before flying to Dublin to meet the Irish taoiseach, Leo Varadkar.

As she shuttled between EU capitals on a whistlestop diplomatic tour aimed at salvaging her deal, the prime minister said the hastily scheduled cabinet meeting would discuss what further steps the government needed to take in the event of a no-deal Brexit.

One cabinet source said ministers had been told they would see “quite an alarming no-deal paper” that would emphasise the need to step up preparations.

With May declining to set a date when her deal will be brought back to parliament for ratification, and her spokesman saying only that it would be before 21 January, France advised its fellow member states that planning for a cliff-edge Brexit had to be their priority.

France’s EU affairs minister, Nathalie Loiseau, on a visit to Brussels, suggested her country’s president, Emmanuel Macron, would urge EU leaders at a summit starting on Thursday to take responsibility for their own preparations rather than be sucked into May’s domestic political drama.

Loiseau said: “We are very concerned about the delay in the vote on the withdrawal agreement, because this withdrawal agreement is the best deal possible, it is even the only possible agreement. It has been negotiated for months.”

Barnier is understood to have given a stark analysis of the situation in a meeting with the European commission president, Jean-Claude Juncker, and his fellow commissioners, suggesting that the danger of a complete breakdown had significantly increased.

The European commission is to publish fresh no-deal warnings next week. During a visit to Berlin, May was reportedly told by the German chancellor, Angela Merkel, that there could be no renegotiation and that any appeals for help should be made in Brussels rather than brought to the capitals.

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Varadkar took the unusual step of suggesting to the Irish parliament that it was still in Downing Street’s gift to prevent a no-deal by revoking article 50 and turning its back on Brexit.

He said: “The option is there to revoke article 50, the option is there to extend article 50 and, where there may not be a majority for anything or at least any deal at the moment in the House of Commons, I do believe there’s a majority that the UK should not be plunged into a no-deal scenario.”

Cabinet sources said the prime minister had warned colleagues on Monday’s cabinet conference call, when she discussed postponing the vote, that reopening the withdrawal agreement would be risky, not least because Varadkar could insist that the Northern Ireland-only backstop be restored to the text.

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May held talks with the Dutch prime minister, Mark Rutte, in The Hague on Tuesday morning before going on to Berlin for talks with Merkel.

The German chancellor reported to the parliamentary faction of the CDU/CSU alliance of which she is a member that she had excluded the possibility with May of reopening Brexit negotiations. “We said that there will be no further opening of the exit deal,” Merkel said.

The prime minister later conducted talks with Juncker and Donald Tusk, the European council president.

Following his meeting with May, Tusk tweeted that the pair had a “long and frank” discussion. “Clear that EU27 wants to help,” he wrote. “The question is how.”

Earlier in the day, Juncker had told the European parliament that there was “no room whatsoever for renegotiation”, but that the EU could offer “clarifications and interpretations” to help the prime minister secure MPs’ support.

Many Labour MPs including the shadow Brexit secretary, Keir Starmer, have argued that there is a parliamentary majority to stop a no-deal exit, calling it a “false choice” between May’s deal and no deal. However, Commons officials believe it would be very difficult in practice.

MPs opposed to no deal had believed one legal route could be to amend the primary legislation, such as an immigration bill, that would be needed for a semi-orderly no-deal exit to allow parliament to insist on an extension to article 50.

Yet experts have come to believe that those amendments may not be within the scope of the bills and that the amendments could not impose conditions on whether no-deal happens or not.