Rishi Sunak was forced into a desperate defence of his new Rwanda asylum law as he battled to hold together the fractured Conservative party amid speculation that he could face a challenge to his position. The prime minister told an emergency Downing Street press conference that he would “finish the job” of getting his controversial deportation plan off the ground despite criticism from the Tory right and anxiety among centrist MPs. The Conservative party chair, Richard Holden, warned MPs that it would be “insanity” to try to oust Sunak over the issue after the resignation of Robert Jenrick, the immigration minister, and denials from Suella Braverman that she was spreading poison in a bid to get rid of him. Yet Sunak faces a rebellion on both flanks of his party as MPs consider whether to vote against the legislation when it comes to the Commons next week, or whether to try to amend it. Sunak said the vote would not be a “confidence matter”, giving Tory MPs who vote against it some leeway and meaning he will not be obliged by convention to stand down or call an election if he loses. Since Labour has stated that it will oppose the bill, it would take just 29 Tory MPs to vote it down. His tetchy appearance in front of reporters followed a chaotic 24 hours during which Jenrick quit, arguing that the proposed law did not go far enough and was a “triumph of hope over experience”. As Sunak has staked his government’s reputation on coming up with a plan to “stop the boats”, Jenrick’s departure was a serious blow to his authority. There has been speculation that at least a dozen Tory MPs are considering submitting letters to trigger a confidence vote. The Tory MP Rachel Maclean, one of several deputy chairs of the party, told GB News that the Rwanda vote would, in fact, be a confidence issue. “Of course it’s about confidence in the government and what it delivers,” she said on Thursday evening. It has emerged that the cost of the scheme had more than doubled to £290m. The Home Office admitted that, on top of the initial £140m payment, it had handed over a further £100m, and extra £50m is to follow. Responding to the news, Yvette Cooper, the shadow home secretary, said: “This is just incredible. The Tories have wasted an astronomical £290m of taxpayers’ money on a failing scheme which hasn’t sent a single asylum seeker to Rwanda. “Britain simply can’t afford more of this costly chaos from the Conservatives.” The emergency bill will give ministers the power to ignore some judgments from the European court relating to asylum, while stopping short of leaving or “disapplying” the European convention on human rights (ECHR) in its entirety. Defending his plans, Sunak claimed his rightwing critics were wrong to say that the bill would not work. He insisted there was only an “inch” between what they were demanding and what the Rwandan government would accept without the scheme “collapsing” entirely. But his critics have argued that the legislation raises the possibility that the Rwanda plan would still be open to individual legal challenges under domestic law. A group of Tory rightwingers are taking legal advice on the bill through the so-called star chamber court process used to assess Theresa May and Boris Johnson’s Brexit plans, before deciding whether to back it or move against it next week. One insider said concerns were focused on clause 4 of the bill, which permits challenges in the domestic courts. They told the Guardian that they planned to back the bill at its second reading on Tuesday, then try to have it amended it at a later stage. However, one MP indicated that they were willing to vote against the bill if it did not incorporate any of the amendments they put forward. “I can’t see how we would support a bill that doesn’t achieve its purpose,” they said. Supporters of the prime minister are furious at the Tory right’s response. One MP described their colleagues as “batshit crazy” and added: “Not a single one of them is a true Conservative.” Sunak also faces a challenge from the centrist One Nation group of MPs, who number over 100, and who sources said were “very nervous” about the draft legislation. It is likely that the legislation will run into trouble in the House of Lords. Edward Garnier, who is advising the centrist One Nation group on the bill, said on Thursday he would vote against the bill. The legislation is “nonsense”, Lord Garnier said, adding that passing a bill to declare Rwanda is a safe country was like passing one saying “all dogs are cats”. However, the attorney general, Victoria Prentis, and the justice secretary, Alex Chalk, who were previously said to have reservations about a hardline approach to the Rwanda plan, are both understood to be “comfortable” with the bill. Allies of the pair said they were reassured that it would not lead to the UK withdrawing from the ECHR. Neither is believed to be considering their position. Richard Holden warned colleagues against jostling for position amid tensions over the Rwanda plan. Echoing the prime minister’s calls for unity, he suggested it was the “biggest challenge” his party was facing ahead of the next election. Asked if he could rule out another leadership contest before the next election, he said: “I think it would be insanity to do that.” The party needed to be “fighting the opposition rather than ourselves”, he said. “We all know that divided parties don’t win elections.” Suella Braverman, who was sacked by Sunak as home secretary, was forced to deny “spreading poison” within the party on Thursday. In a combative interview, she told the BBC she was a “plain speaker” and was not trying to remove the prime minister. However, she refused to back the deportation plan, insisting that “the reality and sorry truth is, it just won’t work”, again warning Sunak of the “perilous” situation the Tories found themselves in given his pledge to stop the boats at the start of the year. “The facts don’t lie, and we need to deliver on a key promise. That’s how we will win the next general election,” she said. “The time for talk, the time for slogans and promises is over. We need to show delivery, and that’s what this debate right now is all about.” Sunak told reporters the bill fundamentally addressed concerns raised by the supreme court over the deportation policy and would guarantee that Rwanda was “unequivocally” safe for asylum seekers. In an attempt to curtail the growing rebellion on the right, he said the legislation would be an “effective deterrent” to people coming to the UK illegally and would restore public trust in the system. The law would end “the merry-go-round of legal challenges” that had blocked the Rwanda plan so far, he said. “We have blocked every single reason that has ever been used to prevent flights to Rwanda from taking off.” He admitted that legal challenges could still be brought against removals, but insisted that the new law left only an “extremely narrow exception” that would require individuals to provide “credible and compelling evidence” that they faced risk of serious harm. The Kigali government has stressed the need for the new UK legislation to be compatible with international law. Sunak said: “If we go any further, the entire scheme will collapse, and there is no point having a bill with nowhere to send people to.” He has appointed two ministers to cover the brief. Michael Tomlinson becomes the minister for illegal migration – attending cabinet – while Tom Pursglove becomes the minister for legal migration and delivery.