Rishi Sunak is engaged in a desperate lobbying push to persuade Conservative MPs to back his Rwanda bill as he hopes to avoid a defeat that could fatally undermine his authority. The prime minister will host an emergency breakfast in Downing Street with members of the rightwing New Conservative group of backbenchers on Tuesday in an effort to reassure wavering MPs. Danny Kruger, the co-chair of the New Conservatives, was one of a number of senior Tories to say on Monday that they did not support the bill in its current form. A Tory source said MPs would use the meeting to tell the prime minister that the bill needs “major surgery or replacement”. The No 10 breakfast follows a series of meetings on Monday involving ministers and factions from the right and left of the party. It was a day of frenetic activity in Westminster reminiscent of Brexit fights from 2017-2019. One person close to the talks described the government’s whipping operation as “belated, panicked and intense”. Sunak himself spent Monday testifying at the Covid-19 inquiry, but Downing Street dispatched the home secretary, James Cleverly, and the illegal migration minister, Michael Tomlinson, to hear MPs’ concerns. Cleverly said after the meeting: “We’re determined to get [the bill] through. It’s important legislation.” If ministers were to be defeated at second reading stage, it would be the first time a government had lost such a vote since 1986, when dozens of Conservative MPs rebelled to defeat a plan by Margaret Thatcher to end Sunday trading restrictions. Many on the right of the party are unhappy with the bill, and say their opposition has hardened since the weekend. One said: “This bill does not work, so I’m not sure why we would back it.” Asked whether they would be willing to trigger a leadership crisis by rebelling en masse, they added: “We don’t want him to go, but if Rishi wants to hold a gun to his own head over this, that’s his decision.” If rightwing MPs decide to oppose the bill, they have the numbers to kill it, with 29 votes against likely to trigger a defeat as Labour is also planning to oppose it. But if the prime minister bows to their calls to amend the bill, Sunak could eventually face an even larger rebellion from centrist MPs from the One Nation group. The group, which comprises about 100 members, said on Monday night they would back the bill “unamended”, adding: “We strongly urge the government to stand firm against any attempt to amend the bill in a way that would make it unacceptable to those who believe that support for the rule of law is a basic Conservative principle.” Sunak has put the Rwanda bill at the heart of his policy to stop people crossing the Channel in small boats – one of five priorities he set out at the start of the year. The legislation is designed to overcome concerns raised by the supreme court, which ruled last month that the policy in its previous form violated domestic and international law. The bill would empower ministers to ignore temporary injunctions raised by the European court of human rights that can stop flights taking off at the last minute. But it does not set aside the European convention on human rights entirely, and would allow individuals to launch legal appeals to argue that they should be spared deportation because of particular circumstances. Tory backbenchers said on Monday they believed these elements of the bill would allow widespread appeals and limit the number of people who would be successfully deported. Mark Francois, the chair of the European Research Group (ERG) of MPs, said on Monday: “The bill provides a partial and incomplete solution to the problem of legal challenges in the UK courts being used as stratagems to delay or defer the removal of illegal migrants to Rwanda. “Rather than plough on regardless, [the government] would be better to pull the bill and to come back with a better draft that doesn’t have all these holes in it.” The ERG published a legal opinion on Monday arguing that the bill left too many paths for people to appeal against being removed. “Experience to date in cases about attempted removal of illegal migrants to Rwanda demonstrated that individual challenges are likely to be numerous, and that they have had a high rate of success,” it said. The government pushed back on this, however, taking the rare step of publishing its own analysis, which said the bill went as far as it could legally and politically. “The government’s approach is tough but fair and lawful,” the document said. “It has a justification in the UK’s constitution and domestic law, and it seeks to uphold our international obligations.” It also defended the decision to allow individuals to appeal against their deportation in British courts. “Not to [allow individual challenges] would mean ministers accepting that those unfit to fly, for example those in the late stages of pregnancy, or sufferers of very rare medical conditions that could not be cared for in Rwanda, could be removed with no right to judicial scrutiny,” it said. By Monday night, the five most prominent groups of rightwing MPs – dubbed the “five families” – had not yet announced which way they intended to vote on Tuesday. While Francois was urging the government to withdraw the bill altogether, others believe their best option is to vote for it at the second reading with a view to amending it later in the process. Sunak said last week that the government could not go further by even an inch as this would collapse the bill because of opposition from the Rwandan government. But his officials and ministers hinted on Monday that there could yet be room for compromise with backbench MPs over elements of the bill. A Downing Street spokesperson said: “We will continue to listen to MPs on their views. Some groups of MPs have set out detailed views earlier today, which we will obviously listen to carefully.” Cleverly told MPs on Monday there was a “narrow landing strip” to make the legislation work, which some believe means there will be room for manoeuvre. While the Tory party remains engulfed in a row over how best to bring down the number of asylum seekers arriving in Britain, the country is continuing to pay the Rwandan government for a scheme that is not yet up and running. Sir Matthew Rycroft, the permanent secretary at the Home Office, told MPs on Monday the government would pay further multimillion-pound lump sums to Rwanda on top of the £290m already pledged. Despite this, he said he had seen “no credible evidence” that the policy of sending people to central Africa offered value for money.