The Government should end the “hostile bureaucracy” facing overseas students and bring in a four-year post-study work visa to help universities overcome Covid-19 and Brexit, a former minister has said.

A predicted large drop in international students due to coronavirus will “expose real vulnerabilities” in university finances and it will compound problems already facing the sector, according to a report.

Jo Johnson, former universities minister, argues that British universities have long been “tied down by bureaucracy, obsessions with poorly-crafted immigration targets and pettifogging rules”.

In a report, published by King’s College London (KCL) and the Harvard Kennedy School, Mr Johnson makes a series of recommendations to the Government on how to reduce the impact on UK universities.

International students should be allowed to stay in the UK for double the length of time after graduating, from two to four years, to “send a clear signal that Global Britain is open to the world” – and the Government should launch a marketing drive to double student numbers from India by 2024, he says.

The report, written by Mr Johnson, also calls for the Government to end “the hostile bureaucracy” facing overseas students by increasing flexibility on visas and English proficiency testing during the pandemic.

It says: “As a first step, the Government needs to recognise the lasting damage that has been done since 2010 by the inclusion of overseas students in the UK’s target of annual net migration of under 100,000 and by the welter of Home Office visa restrictions and hostile bureaucratic barriers to study and post-study work that have had the intended effect of deterring applicants.

“These have done substantial reputational damage that will take continued commitment to reverse.”

Mr Johnson was universities and science minister until September last year when he resigned from his brother’s Cabinet citing an “unresolvable tension” between his family loyalty and the national interest.

Mr Johnson, president’s professorial fellow at KCL and senior fellow at the Harvard Kennedy School, said: “International education is one of the UK’s few globally competitive sectors. Income from it makes it possible to undertake loss-making research and deliver strategically-important lab and studio-based courses costing more than domestic fees.

“To secure our post-Brexit future as a knowledge economy and trading nation, we need to go all out to achieve ambitious education export goals.”

Vivienne Stern, director of Universities UK (UUK) International, said: “Given current pressures on universities and the difficulties they are likely to face in the short-term given the current pandemic, the recommendations are timely – and a response from Government urgent.”

A Department for Education spokeswoman said: “We are proud that so many international students come to the UK every year to study.

“The UK’s universities thrive on their global reputation as home to some of the very best institutions in the world.

“Our universities remain open to all international students and we will have a first class offer for students through the introduction of the new graduate route, which will permit university graduates to remain in the UK to work or look for work for two years post-study.”