Rebel Conservative MPs’ plans to oust Boris Johnson next week have descended further into disunity, with some worried that potential contenders to replace the prime minister are not ready to launch their bids. One MP hoping to engineer defeat for Johnson is now encouraging colleagues to withdraw their letters of no confidence to avoid triggering a vote “by accident” as soon as Monday or Tuesday, the Guardian has learned. The speed of the backlash against the prime minister after the Sue Gray report on Covid law-breaking in Downing Street has surprised many, given the lack of coordination by rebels. More than 45 Tory MPs have publicly questioned Johnson’s fitness to hold office. Some MPs told the Guardian they intended to submit a letter calling for a vote on Johnson’s premiership on Monday, to reach the required 54-letter threshold to trigger a ballot but avoid overshadowing the Queen’s platinum jubilee this weekend. However, those who are wargaming how such a vote would play out are conflicted about the best time to force it. Some said they were concerned that would-be leadership candidates had not yet mobilised supporters to summon the 180 votes needed for Johnson to lose a no-confidence vote. They fear that if Johnson wins the contest narrowly, he will refuse to step down and will be protected for a year. They reason that MPs should hold off submitting letters until after two byelections on 23 June, viewed as tests of the prime minister’s election-winning abilities. A source said Johnson still had the cabinet “wrapped around his finger” and that ministers viewed as being potential successors were “all too scared”. Others are frustrated the campaign to oust Johnson has dragged on for months, and believe the aftermath of the Gray report is the moment to challenge his authority. They hope that the prospect of a narrow victory for Johnson, that could leave the Tory party in paralysis in the runup to the next general election, will be enough to convince ministers to vote against him. An agitated rebel lamented the lack of coordination among those who want Johnson out, saying: “Give me a Bond villain, for Christ’s sake.” The former Conservative leader William Hague predicted MPs were “moving towards having a ballot … either next week or around the end of June”. Robert Hayward, a Tory peer and polling expert, said: “If I was a plotter, I’d probably want it to go on for a while because it allows the conversations to take place longer. The byelections on 23 June, in Wakefield [and] in Tiverton and Honiton, will be key. “If I was a Boris fan, I’d probably want it as quickly as possible to get it out of the way because 54 is relatively easy. One hundred and eighty, which is the number on a vote of confidence, is a different matter.” Johnson’s allies dispute that he is likely to face a confidence vote, with the home secretary, Priti Patel, calling the campaign against him a “sideshow” and telling rebels: “Forget it.” She said: “We need to concentrate on doing our jobs. Our job is to deliver on the people’s priorities. They won’t thank the Conservative party for talking about itself at a time when people have anxieties, concerns, apprehensions.” A government source said “those complaining don’t understand how much British politics has changed since 2016, and Boris has been at the heart of that”, adding: “The parliamentary party as a whole gets it, and that’s why they are backing him.” However, all members of the government payroll cannot be relied upon to back Johnson in a leadership contest. It is understood that at least two have privately submitted letters of no confidence. Meanwhile, Andrew Bridgen, a backbench MP who said he recently resubmitted his letter after withdrawing it when the war in Ukraine began, speculated in a message sent to a Tory WhatsApp group that No 10 would be told on Monday morning the 54 letters threshold had been reached. In a message seen by the Guardian, he said he thought a confidence vote would be held on Wednesday, and added: “The PM may well win, but the vote against him will be larger than he expects as it is a secret ballot.” Graham Brady, chair of the 1922 Committee of backbenchers and the MP to whom letters are submitted, declined earlier this week to comment on whether the threshold was close. ““I shall retain my discretion,” he said.