Academics are already planning to leave the UK in the face of uncertainty on their rights after Brexit, university leaders have claimed.
The leaders of 35 Oxford University colleges have warned that the institution will suffer "enormous damage" if European Union staff lost their right to work in Britain.
They urged the Government to back a House of Lords amendment to the Brexit Bill which guarantees protections for EU nationals living in the UK.
In a letter to The Times, signed by vice-chancellor Professor Louise Richardson and all but three Oxford college heads, they said the Government's promises have not provided reassurance.
"Oxford University relies on EU citizens as lecturers, researchers and support staff. If they lost their right to work here, our university would suffer enormous damage which, given our role in research, would have reverberations across the UK," they wrote.
"Our EU colleagues are not reassured by a government which tells them that deportation is not going to happen but declines to convert that assurance into law; some are worried, some are already making plans to leave.
"Many of our staff don't know whether absences abroad on research contracts will count against them. Others do not know, however longstanding their work and residence, whether their children will be able to remain in the UK."
Almost a fifth of UK academics in 2015/16 were from the EU.
MPs are expected to throw out the changes to the Brexit Bill made by peers when it returns to the House of Commons on Monday.
The bill will then go back to the Lords and, providing peers allow it to pass, the Prime Minister could trigger Britain's divorce from the EU as early as Tuesday.