Brexit has worsened the UK’s acute shortage of doctors in key areas of care and led to more than 4,000 European doctors choosing not to work in the NHS, research reveals.

The disclosure comes as growing numbers of medics quit in disillusionment at their relentlessly busy working lives in the increasingly overstretched health service. Official figures show the NHS in England alone has vacancies for 10,582 physicians.

Britain has 4,285 fewer European doctors than if the rising numbers who were coming before the Brexit vote in 2016 had been maintained since then, according to analysis by the Nuffield Trust health thinktank which it has shared with the Guardian.

In 2021, a total of 37,035 medics from the EU and European free trade area (EFTA) were working in the UK. However, there would have been 41,320 – or 4,285 more – if the decision to leave the EU had not triggered a “slowdown” in medical recruitment from the EU and the EFTA quartet of Norway, Iceland, Switzerland and Lichtenstein.

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Record numbers of nurses and midwives from EU27 countries quit Britain last year, fuelling fears that a Brexit brain drain will deepen the NHS’s already chronic staffing crisis.

A total of 3,962 such staff from the European Economic Area (EEA) left the Nursing and Midwifery Council register between 2017 and 2018. The register tracks who is eligible to work in those areas of healthcare in the UK.

The number of departures was 28% more than the 3,081 who left in 2016-17 and three times higher than the 1,311 who did so in 2013-14, the first year the NMC began keeping data on such departures.

At the same time, the number of EU nurses and midwives coming to work in the UK has fallen to its lowest level. Just 805 of them joined the NMC register in 2017-18. That total is just 13% of the 6,382 who came over the year before.

“It feels that efforts to boost the number of nurses are being dragged down by a botched Brexit,” said Janet Davies, the chief executive of the Royal College of Nursing.