Rishi Sunak risks damaging “cultural security” and faces defeat at the next general election unless emergency measures to curb net migration are introduced, a new group of Conservative MPs has warned. As Downing Street slapped down the group’s proposals to cut visas issued to care workers, members of the New Conservatives grouping said that ignoring their 12-point plan could end in electoral defeat. The comments were made at a launch event of the organisation’s plans to cut net migration from 606,000 to 226,000 before the end of 2024. The proposals, backed by 20 MPs including allies of Suella Braverman, the home secretary, have been widely reported as undermining the authority of the prime minister. Miriam Cates, the MP for Penistone and Stocksbridge – who co-chairs the group, told the event: “Failure to keep numbers down despite a clear mandate and repeated promises raises deep concerns about national and cultural security and sovereignty and democracy.” She then warned Sunak of the consequences of ignoring immigration, which she said was a vital issue for voters in red wall constituencies. “The choice is this: cut immigration, keep our promise to voters and restore democratic cultural and economic security. Or kick the can down the road, lose the next election and resign ourselves to a low growth, low wage, labour-intensive service economy,” she said. The proposals follow party anger over official figures released in May that showed total long-term immigration was at a record high of 1.2 million people, while emigration was 557,000. The rise had been largely fuelled by people from outside the EU entering the UK to study, work or escape conflict or oppression. Lee Anderson, the deputy chair of the Conservative party, pulled out from the launch of the proposals, after telling colleagues that he was sick. Measures put forward by the New Conservatives include closing temporary schemes that grant eligibility for worker visas to “care workers” and “senior care workers” to reduce long-term inward migration by 82,000. They also propose stopping graduating overseas students from staying on in the UK for up to two years to find work. The government has no plans to remove care workers from the shortage occupation list to cut immigration despite calls from Tory MPs, Downing Street said. No 10 also downplayed the prospect of blocking foreign university students from staying in the UK after graduation. The prime minister’s official spokesman refused to say whether Sunak was frustrated by Anderson’s support of tougher migration rules but acknowledged there were “different views on each side”. Asked whether care workers could be removed from the shortage occupation list, the official replied: “That’s not an approach we’re considering currently. Again, we know there is significant demand in the care sector for staff.” Yvette Cooper, the shadow home secretary, asked Braverman in the Commons: “Will the home secretary wish the deputy chairman of the Conservative party a speedy recovery from the terrible sick bug which I understand has prevented him from launching this morning an entirely different Conservative immigration policy to the policy of the Conservative home secretary? “And does she agree with him that social care visas should be cancelled – yes or no?” Braverman sidestepped the question and claimed Labour wants “open borders and unlimited migration”, adding: “There’s a real malaise descending upon the Labour party, they don’t even know what they think, to be honest.”