The UK’s top universities will today publish 10 demands on EU citizens’ rights which they say Theresa May must meet to ensure higher education is not damaged by Brexit.

In a hard-hitting document passed to The Independent, the 24-strong Russell Group – including Oxford, Cambridge and London universities – warn Ms May her current approach is hurting a sector which generates £73bn a year for the economy.

They call on the Prime Minister to scrap her plan to make every single EU citizen apply for a new “settled status” and instead to grant an automatic right to remain to thousands of people already permanently resident here.

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The internationally renowned institutions also demand she rethinks her plan to strip some EU citizens of the right to remain, if they leave the country for more than two years.

It comes amid an impasse in Brexit talks over EU citizens’ rights, with Brussels having rejected Ms May’s opening proposals on an issue which should have presented an opportunity for an early agreement.

In the paper handed to The Independent, the Russell Group sets out 10 points “requiring greater clarity” over the Government’s plans, which it says have left “a significant degree of uncertainty ... concerning EU nationals’ rights and the process for acquiring them after the UK leaves the EU”.

It adds: “Whilst this is the UK Government’s first position for the negotiations, this lack of clarity is causing considerable concern for EU nationals at our universities and impacting on our ability to recruit talented staff from the EU.”

Under Ms May’s current plans all EU citizens will have to go through an application process to determine what rights they are eligible for after Brexit, but the Russell Group said this is unnecessary.

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Among the universities’ demands is one that all EU citizens currently holding permanent residence are transferred automatically to a new “settled status” promised by the Government, without the need for any new assessment.

They also say that where it is possible for the Home Office to identify those eligible for the settled status from existing recorded data, individuals should also automatically be transferred, removing uncertainty.

Jessica Cole, head of policy for the Russell Group, said: “Brexit is causing uncertainty and anxiety for EU staff, who need clarity over their future rights as soon as possible.

“There are around 25,000 members of staff from other EU countries at Russell Group universities delivering high-quality teaching and cutting-edge research. We value our EU colleagues and want them to stay.”

She added: “There is no reason why individuals and families who have already secured permanent residency should not be granted the new settled status automatically.”

Leading academics have long expressed fears of a Brexit brain drain in the higher education sector, with more than 1,300 academics from EU countries reported to have left UK universities in the past year.

Ms May’s plans also set out how EU citizens could be stripped of their settled status if they leave the country temporarily after Brexit, with the small print stating that someone could lose their right to remain if “absent from the UK for more than two years, unless they have strong ties”.

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The Russell Group document calls for academics and students to be exempt from the restrictions while they spend time abroad for study or research and for a broad interpretation of what “strong ties” means.

Professor Stuart Corbridge, the vice-chancellor of Durham University, said: “Students, academics and professional services staff from across the EU have helped make Durham a world leader in higher education.

“Universities and European staff need to be able to plan for the future with confidence and an early agreement on the permanent rights of EU citizens is vital”.

Other points on the group’s list are that a “grace period” for EU citizens trying to regularise their status should be extended if Government systems cannot process applications fast enough, that costs should be kept to a minimum and that guidance should be produced for businesses.

Oxford University is a member of the Russell Group, demanding changes to Ms May’s plans ( Getty )

They demand all EU students starting courses in 2017/18 and 2018/19 are given the chance to stay for five years and gain settled status, that more clarity is given around the rights of families and children and that qualifications obtained before Brexit continue to be recognised across borders.

Professor Sir Anton Muscatelli, vice-chancellor of the University of Glasgow, said: “Brexit is causing significant anxiety for EU staff.

“There are still a number of areas where greater clarity over the UK Government’s offer to European citizens is required. The sooner that we get answers for EU students, staff and their families, the better it will be for everyone.”

A final demand is that the Government make clear when the “cut off” date will fall, after which new arrivals from Europe may not be guaranteed the chance to achieve settled status.

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A Government spokesperson said: “We have been clear about our commitment to the UK’s world-class higher education sector.

“The Government wants to reach a reciprocal agreement for EU citizens in Britain and UK nationals in Europe as quickly as possible. We are developing a new application process and will ensure that it is as light-touch, streamlined and user-friendly as possible.

“We recognise that there are a wide range of individual circumstances to consider and we will continue to engage with the sector as this work develops.”

The European Parliament which has the power to reject any Brexit deal has also said it will veto Ms May’s proposals if they do not improve.

Angela Rayner, the Shadow Education Secretary, said: “This Government’s shambolic handling of this issue has created huge uncertainty for universities, staff, and students.

“The Tories’ Brexit chaos means that universities are in danger of losing the best staff and students without clarity about their right to remain in Britain.