Brexit is contributing to a serious brain drain in UK universities, say the Liberal Democrats, after it emerged that almost 11,000 EU academics had left since the 2016 referendum.

The figures, based on freedom of information responses from universities, show 10,918 left in the three years starting with the 2016-17 financial year. In 2018-19, 4,014 quit, 31% more than in 2015-16, and 40% more than in 2014-15.

The figures are almost certain to be underestimates of the real total, because the study is based on 81 universities that responded to the requests. Universities UK, the main representative body for the higher education sector, has 136 members.

Numbers varied significantly between institutions. The Royal Central School of Speech and Drama in London reported no EU staff leaving, while Oxford University said 1,515 had done so over the three years. Edinburgh University saw 1,271 depart, and Cambridge 1,292.

Universities have introduced measures to try to keep EU academics in place, with Oxford saying a year ago it would pay any administrative costs for staff from EU countries and their families to stay in the UK permanently after Brexit.

The Lib Dem statistics only cover departures, and not EU nationals entering the UK to take up academic posts. Figures from the Higher Education Statistics Agency show that the overall number of EU academic staff rose slightly between 2016-17 and 2017-18, the most recent data available, from 35,920 to 37,255.

However, the sector has previously warned that Brexit is likely to harm the country’s universities because of factors including uncertain immigration procedures and the loss of research funding.

In September, Universities UK said a survey of members had found that almost 60% had lost existing or potential staff to overseas institutions; 55% had seen a change in their level of collaboration with other countries; and 50% had experienced a change in demand from EU students.

In a briefing on Boris Johnson’s departure plan, Universities UK said that while it was greatly preferable to a no-deal Brexit, the sector still faced potentially losing out on academic talent, as well as being hit in areas such as research collaboration and access to funding, and sending students abroad as part of their degree.

Separately, in October the Royal Society said the UK’s share of EU research funding given out per year has fallen by almost a third since 2015.

Layla Moran, the Lib Dems’ education spokeswoman, said it was “deeply concerning that Brexit has already driven so many talented academics to abandon the UK”.

She said: “Our universities are being threatened by a Brexit brain drain, exacerbated by Boris Johnson’s reckless promise to crash us out of the EU by 2020 no matter the cost.”

“This is sadly not surprising given the Tory party has adopted the xenophobic rhetoric of Nigel Farage, making our colleagues, friends and family from the EU feel unwelcome.”