The former UK immigration minister Robert Jenrick has said he will not vote for Rishi Sunak’s bill aimed at deporting asylum seekers to Rwanda this week, in a blow to the prime minister. Jenrick, who resigned over the bill, said it would not work and needed to go further in setting aside human rights law if it was to have a chance of getting the Rwanda scheme to work. “I won’t be supporting this bill, but I do think we can fix this, and that’s what I want to do now,” he told the BBC’s Sunday With Laura Kuenssberg. “I care about this policy because I care about border security and I’m determined that we can persuade the government and colleagues in parliament that there is a better way.” Sunak is facing a severe test of his leadership when the bill comes to the Commons on Tuesday, as it will fail if only 28 MPs vote against the legislation. Its passage is likely to hinge on whether Jenrick, Suella Braverman, the former home secretary, and their supporters on the right of the party decide to vote against it or abstain. The last time MPs voted against legislation at second reading – the first stage of a bill – was in 1986 under Margaret Thatcher. With his flagship legislation in trouble, there is growing talk of the ousting of the prime minister before the election by plotters within his own party. Some backbenchers are keen to reinstall either Boris Johnson or an ally of Liz Truss, the former prime minister. Johnson is no longer in parliament but some MPs think he could return in a byelection if Sunak were removed, with others pushing for him to team up with the Reform politician and former Ukip leader Nigel Farage. The Mail on Sunday reported this weekend that his critics within the Tories were planning “an Advent calendar of shit” to destabilise his leadership in the run-up to Christmas. Jenrick may be joined in voting against the bill by members of the hard right of the party, whose “star chamber” of lawyers led by the veteran Eurosceptic Bill Cash is believed to have come to the conclusion that it will not work. Cash wrote in the Sunday Telegraph that they had been considering whether the “wording is sufficiently watertight to meet the government’s policy objectives”. “At present it does not,” he added. “Our report, I hope, will be helpful to the government in deciding whether the bill in its current form is fit for purpose or will require further amendment, even by the government itself.” His comments open the door for Sunak to promise further amendments to harden the legislation at a later stage – but doing so could alienate the One Nation group of the party who say the bill comes close to unacceptably undermining human rights law. Centrist Tory MPs who are concerned the bill sets aside human rights laws are likely to vote in its favour at second reading in the hope of making changes further down the line. They are due to meet on Monday to decide if the legislation is compatible with international law. Michael Gove, the communities secretary, insisted top lawyers had said the government’s new legislation aimed at sending asylum seekers to Rwanda was “sound”. Speaking to Sunday Morning With Trevor Phillips on Sky News, Gove suggested his party had had a “relative success” already in responding to irregular migration, which reached a record high this summer. “It’s pretty tough actually if you look at what we’re saying,” he said. “Of course we will look at what any colleague and, indeed, any eminent lawyer says, but whether it’s Jonathan Sumption or David Wolfson, they are pretty clear, this law is sound.” He also insisted the government was “not contemplating” holding a general election if the legislation were voted down. Many Conservative MPs are very anxious about the idea of a plot against Sunak before going to the polls, as getting rid of him would bring in a third unelected prime minister since the last election. Damian Green, the leader of the One Nation group of MPs and a former deputy prime minister, said those wanting to remove Sunak were “mad, or malicious, or both”.