Rishi Sunak risks ripping up the Northern Ireland peace process if he blocks human rights laws so the UK can deport asylum seekers to Rwanda, senior Conservatives have said. After similar concerns from the White House on Thursday, the MPs said widely reported plans from Downing Street to disregard parts of the Human Rights Act could undermine the Good Friday agreement and damage UK-US relations. The warnings come as the prime minister is under increasing pressure from right-leaning MPs and ministers to close off legal avenues to asylum seekers who have successfully challenged their removal to Rwanda. The government is expected next week to revive the Rwanda policy of sending people seeking asylum to east Africa after the supreme court ruled that the plans were unlawful. Sunak believes the government can address the court’s concerns with a new treaty with Rwanda, which could be signed next week by James Cleverly, the home secretary, and emergency legislation to block future legal challenges to the policy. In an interview with the Times, Cleverly acknowledged he has become “frustrated” with the focus on Rwanda and that it should not be seen as the “be-all and end-all”. He said while it is an “important” part of the plans and will deter people from crossing the Channel in small boats, it is part of a broader strategy. Cleverly also said he believes leaving the European convention on human rights (ECHR) would jeopardise “key cooperation” with other countries including France, which has helped addressed illegal crossings into the UK. The New York Times reported on Thursday that senior White House officials were concerned that a block on legal challenges would damage the authority of the ECHR which is fundamental to the Good Friday agreement. Conservative Sir Bob Neill, chair of the justice select committee and a former minister, said he had similar concerns that attempts to block human rights laws would damage the authority of the ECHR and risk peace in Northern Ireland. “We have known for a long time that laws such as the European convention on human rights are a central part of the Good Friday agreement,” he said. “Anything that undermines the Good Friday agreement would be really dangerous for the peace process. There is no à la carte menu, where you can pick and choose which parts of the convention you wish to follow.” Asked if he agreed with reports that dozens of Tory MPs could vote against any attempt to undermine human rights laws or the ECHR, Neill said: “Yes. There is a very strong feeling that we have to be proportionate about this. We want to stop the boats. But we can’t rip up our international obligations.” A minister told the Guardian that there would be resignations from the government if any attempt to block human rights laws undermined the Good Friday agreement. “This agreement is fundamental to our place in the world. We all know what it means to Joe Biden. We are a government which believes in international law, and – I hope, I believe – the prime minister agrees,” the minister said. The development comes after Sunak refused to apologise after record levels of net immigration appeared to break a key election promise. Official figures on Thursday showed the difference between the number of people coming to live in the UK and those leaving had peaked at 745,000. In an interview at the Nissan car plant in Sunderland, Sunak declined to comment when asked if he would apologise for not meeting the manifesto pledge. “I’m very clear that the levels of migration are too high and they’ve got to come down to more sustainable levels,” he said. The immigration minister, Robert Jenrick, put forward a five-point plan to No 10 that included proposals for a required minimum annual salary of £35,000 in order to receive a work visa and a cap on the total number of visas for NHS and social care workers. Madeleine Sumption, the director of the Migration Observatory at the University of Oxford, said both proposals could struggle to bring down the numbers, especially if there is not exemption for care workers. “The fundamental problem, and one that the immigration system cannot fix, is that care is poorly funded and the pay and conditions are not good enough to attract British workers into difficult and stressful jobs,” she said. “And the last time there was cap on skilled workers, the government dropped it as soon as it began to bite because it caused all sorts of operational difficulties.” Downing Street refused to say what Sunak makes of Jenrick’s proposals when asked by journalists, insisting No 10 would not be getting into “running commentary on policy development”. Boris Johnson said in a newspaper column that he would have raised the minimum salary threshold to £40,000 a year. “We have the powers to sort it out, and to change our immigration rules – which is exactly why the British people voted to take back those powers in 2016,” the former prime minister wrote in the Daily Mail. Johnson left office last year and in 2019 promised in his manifesto that “overall numbers will come down”. The ONS said on Thursday that the difference between the number of people legally arriving in Britain and those leaving was 745,000 in the year to December 2022. The figure is three times higher than the levels seen before Brexit. Many MPs on the right of the party, including the former home secretary Suella Braverman, have called on Sunak to honour the commitment to reducing the numbers. Calls to curb the number of foreign workers in the NHS and social care are likely to be met with resistance by health officials amid chronic staff shortages across the health and care sector.