Image copyright iStock Image caption Universities have been worried about keeping their international staff

Almost a third of university academics in the UK are from outside the UK, according to figures published by the Higher Education Statistics Agency.

And almost one in five is from a country in the European Union.

University leaders have been concerned that Brexit will make it harder to recruit and retain staff from the EU and around the world.

There has also been a "significant reduction" in overseas students in the latest migration figures.

Competing for staff

Universities have warned that they depend on being able to recruit highly-mobile international staff and students - and these latest figures show the extent to which they could be affected by changes in immigration rules.

The analysis of academic staff shows that 29% are from outside the UK - and in some areas, such as engineering and technology, non-UK academics account for 42% of staff.

In maths, physics and biology, 38% of staff are non-UK, with most of these from EU countries.

When the education select committee took evidence from universities about the likely impact of Brexit, they heard fears that talented and sought-after mathematicians from the EU could move elsewhere.

Prof Catherine Barnard, from the University of Cambridge, told MPs that her own university had seen a 14% drop in applications this year from EU students - and warned of the risk of a perceived "anti-immigrant sentiment".

In the humanities, 35% of academic staff are from overseas, most of them from EU countries, according to the Statistics Agency figures.

There was also evidence of a downturn in overseas students coming to the UK, in figures published by the Office for National Statistics.

There was a fall of 41,000 recorded - with the decline mostly among students from Asia.

China accounts for the biggest number of overseas students coming to the UK - followed by the United States and India.

"There has been a statistically significant decrease in non-EU long-term students immigrating to the UK while a small increase was seen in the number of study visas issued," said Nicola White, head of International Migration Statistics at the ONS.

But there were also questions about how student migration is measured and how students leaving the UK after their studies might be accurately counted.

The ONS is planning to investigate this "significant challenge" and to introduce a new online student survey.

University leaders have campaigned to remove students from net migration targets - and have warned of the financial risks if overseas students are deterred.

Alistair Jarvis, deputy chief executive of Universities UK, said much of the success of UK universities depended on the "ability to attract talented staff from around the world".

"The government must ensure that the UK is welcoming to EU and international staff and that we can continue to access valuable and collaborative European research networks."

Universities Minister Jo Johnson, writing to the higher education funding council, said: "Overseas students and staff, including those from the EU, make a crucial contribution to our universities and we want that to continue."