Rishi Sunak is facing an immediate backlash over plans for a “mindless crackdown” on overseas students, as three former Tory university ministers warned it would hit attempts to level up the country and hold back Britain’s faltering economy. Tory discontent is growing on several fronts just weeks into Sunak’s premiership, with rebellions growing this weekend over housebuilding plans and his vow to keep a ban on new onshore windfarms. In another sign that Sunak is struggling to hold his party together, senior Tories are now raising the alarm over his plans to clamp down on the number of international students coming to Britain in the wake of last week’s record net migration figures. Downing St has raised the prospect of limiting visas for students coming to complete “low-quality” degrees. Three Conservatives who served as universities minister over the last decade all told the Observer they had serious concerns about the plans. Jo Johnson, Chris Skidmore and David Willetts said it would hit the UK’s reputation, growth, and the levelling up agenda. They also said it risked undermining the financial viability of Britain’s higher education sector. “Other countries look with envy at the UK’s appeal to global talent,” said Johnson. “Higher education is one of our few globally competitive sectors and strong demand reflects its high standing in countries that are central to our post-Brexit positioning, including India. Finally, it’s hard to imagine a policy more likely to harm UK ambitions to become a science superpower and to level up across the country than a mindless crackdown on international students.” Skidmore, who set out the last international students strategy as universities minister and is now overseeing an independent commission on the issue, said the UK should be growing the sector, rather than attempting to shrink it. “It would be a disaster for international student populations to shrink in areas like Preston or Newcastle, or anywhere else where there’s a regional university,” he said. “Domestic students are subsidised now by international students. International students also massively subsidise research and development in universities. “To pull the plug would potentially destabilise the future of the UK economy, it would destabilise the ability to level up areas which are seeing inward investment from international students, and it would destabilise the UK role in the world, post-Brexit.” Willetts said it was wrong to try to effectively penalise less prominent universities offering specialised courses to overseas students. “The so-called ‘good’ universities are prestigious and do world-class research, but there are universities with different missions: focusing on more technical education, training nurses and teachers, doing applied research with local employers,” he said. “Unfairly regarding them as “bad” is the kind of snobbery which feeds Britain’s skills crisis. It would be wrong to deprive them and their communities of revenues from overseas students.” There is also concern among the most prominent figures in the sector. Michael Spence, president and provost of UCL, said Britain was already fighting off “stiff competition” from other nations to attract students: “Our international students also bring fresh ideas, a diverse cultural and social perspective and extensive global networks, which benefit UK students. We need to do everything we can to ensure that Britain remains an open and welcoming place for these students.” The net migration figure of 504,000 over the 12 months to June 2022 came after home secretary Suella Braverman’s vow to bring it down to the tens of thousands. Students accounted for the biggest proportion of immigrants, with 277,000 coming during that time. The backlash shows the challenges Sunak already faces in trying to quell party dissent after a period of infighting that has seen the party plunge in the polls. While No10 is desperately trying to avoid any issues that risk political divisions, major clashes could emerge in the coming weeks.Ministers have already been forced to delay a vote on housebuilding targets after the threat of a Tory rebellion. More than 50 Tories have now signed up to an amendment opposing targets. Opposition is also building against Sunak’s ban on new onshore windfarms. Boris Johnson and Liz Truss are backing the amendment to the levelling up and regeneration bill, which could be voted on before Christmas. Simon Clarke, the former minister behind the move, said support was growing across the party. Alok Sharma, the Cop26 president, is the latest to announce his support. Clarke told the Observer: “I’m delighted by the really strong showing that this amendment has secured among Conservative MPs from all wings of the party. A lot of attention has rightly been grabbed by Boris and Liz backing this, but it is something which speaks to One Nation and Thatcherite traditions alike because it’s pro-growth and pro-green. The economics of the situation make the case unanswerable. But even if colleagues don’t like this, we have to recognise that we either address this issue now or a Labour government will one day do so in a way which does less to protect community rights.” A Labour source said that the government had “put party before country and abandoned their main piece of legislation because they’re scared of their own backbenchers”. They added: “This bill is far from perfect, but the reality is that levelling up is the route to creating growth and this is their only plan for it.”