For students, the possible demise of the Erasmus exchange programme was a “catastrophe”, she wrote. Also, negotiators must ensure that German students continue to be eligible to pay local fees - much lower than the costs for non-EU foreign students.

Some 14,000 German students are currently enrolled at British universities.

For academic staff, the Brexit vote has caused “painful” uncertainty as to whether they will even be able to get residence permits.

“Some top academics are not accepting posts in British universities as they do not know the conditions under which they will be able to work here in the future,” she wrote.

More than 5,000 Germans work in British universities out of a total of roughly 32,000 EU-national staff - 15 percent of the total number of academic staff in the UK.

She promised that her organisation, which represents 239 institutions and 105 student bodies, would continue to campaign for “continuity, expansion and openness of academic exchange”.

EU franchises

Her comments echo warnings from UK institutions over the consequences of Brexit.

Dame Julia Goodfellow, president of industry body Universities UK, recently called for “'swift and positive action” to reassure EU students that they would be eligible to pay local fees in the coming years.

Warnings over the future of research funding have abounded since the referendum.

A group of institutions issued a joint statement in July urging the government to safeguard research and collaboration with the EU.

Their statement highlighted that the UK had received €6.9 billion in EU research grants between 2007 and 2013, and that most overseas collaborations undertaken by British academics were with EU colleagues.

British universities have already begun to explore possibilities including setting up campuses in the EU as a sort of franchising – a strategy some already follow in India, China and elsewhere.

In a recent speech at Nottingham Trent University, UK universities minister Jo Johnson said EU students starting studies this autumn would remain eligible for local fees and they would be able to use the UK student loans system.

And he said the UK Treasury would underwrite all EU research funding awarded while the UK remained a member of the bloc, though uncertainty remains over what kind of funding will be available after Brexit.

But he conceded that he could provide no further clarity for academic staff from the EU, nor could he give any guarantees for students planning to come to the UK next year.

“These issues are inevitably closely linked to the wider process of exiting the and the sequencing is important to get right,” he said.