A surge in the number of Polish people and other European citizens leaving the UK since the Brexit vote means there has been an 84,000 drop in net migration to the UK, to 248,000, the lowest level for nearly three years.

The Office for National Statistics said the fall in net migration in 2016 was driven by a 40,000 rise in emigration compared with 2015, mainly of EU citizens, and a fall of 43,000 in immigration.

The immigration drop was partly due to 25,000 fewer Poles and other eastern Europeans – citizens of the A8 countries – coming to work in Britain, possibly put off by the referendum vote, and a 16,000 rise in the number of them leaving. Net migration from the A8 was 5,000 last year – the lowest level since those countries joined the EU in 2004.

Uncertainty over their future legal status in Britain has also triggered a rise in the number of EU nationals and their family members applying to the Home Office for permanent residence and other documents. More than 103,000 decisions were made in the first three months of this year compared with 77,000 between October and December 2016.

Home Office figures show the number of decisions has accelerated sharply since the Brexit vote, with 235,000 resolved since June.

The latest figures show the majority of decisions result in applicants are being issued with residence cards or other documents, with more than 78,000 successful applications out of the 103,000 decisions between January and March this year. Just over 18,000 had their applications refused and 6,500 received an initial rejection and were asked to apply again.

The rapid rise in permanent residence applications indicates the degree of uncertainty being caused by Britain’s refusal to guarantee the rights of EU nationals after Brexit.

The sharp fall in the politically sensitive net migration figure will provide some relief for Theresa May, whose decision to renew the 100,000 net migration target in the Conservative manifesto was attacked by the former chancellor George Osborne as “economically illiterate”. It is still far above the target – but for the first time since 2012 the numbers have actually started to fall.

The drop in immigration included a further 32,000 fall in international students in 2016 to 141,000, not far from the lowest levels seen since 2002.

Work remains the most common reason people come to live in Britain. More than 275,000 came to work in 2016, and the majority, 180,000, had a definite job in place. Fewer migrants came without a specific job to come to, but looking for work; that figure came down by 35,000 to 95,000 in 2006.

The Home Office said regular quarterly transparency data showing the scale of the backlog of applications or “work in progress” from EU nationals was not being published for the first time.

Euan Smith, an employment partner at Pinsett Masons, said: “The sharp increase of EU citizens leaving the UK and the decline of incoming EU migrants underscores the significant impact Brexit has already had on businesses in the UK. Those that rely heavily on EU migrant workers, including construction, engineering and the medical profession are likely to be the hardest hit.

“The number of people entering the UK for work has dipped, yet it remains far in excess of the UK government’s ambitious plans to reduce net immigration to the ‘tens of thousands’. Indeed this reinforces the view that Brexit is not the immigration silver bullet that some hope and expect it to be. If the government wants to achieve its target, a more comprehensive review of immigration rules will be crucial.”

Sarah Stevens, the head of policy of the Russell Group of universities, said the figures suggested there has been a clear increase in the number of EU nationals leaving the UK ahead of Brexit talks.

“We would be concerned if this national trend reflected a loss of talented EU staff working in UK higher education due to uncertainty over their future rights. As a priority, government should confirm that existing work and residency rights will be protected.

“This would help make clear that current EU nationals are welcome in the UK. In the longer term, we need an immigration regime which ensures UK universities can recruit and retain talented staff and students from across the EU and more widely without bureaucratic visa burdens.”