The number of EU citizens leaving the UK is at its highest level for a decade with 130,000 emigrating in the year to September, figures show.
But 220,000 EU nationals still moved to Britain over the same period, the Office for National Statistics found.
It means net EU migration – the difference between arrivals and departures – was 90,000, the lowest for five years.
The ONS said Brexit could be a factor in people’s decisions to move.
Nicola White, head of international migration statistics at the ONS, said migration was complicated and could be influenced by lots of different reasons.
The figures also show that more British people are emigrating than are returning to live in the UK.
Of those EU nationals arriving in the UK, fewer were coming for “work-related reasons”, in particular to “look for work”.
By contrast, immigration from countries outside the European Union is going up which means the UK population is continuing to grow at a similar level to early 2014.
Some 285,000 non-EU citizens arrived in the UK in the 12-month period to September, and 80,000 departed.
This gives a net increase of 205,000, the highest for six years.
BBC home affairs correspondent Danny Shaw said this was largely driven by more people coming to study in the UK and an uncharacteristic dip in the previous year’s figures that may have been corrected.
He also speculated whether firms were starting to struggle to recruit or retain people from the EU, forcing them to look outside the EU.
Overall, net migration is estimated to have fallen by 29,000 to 244,000 in the same period.
This includes 73,000 British people coming back to the UK and 125,000 Britons leaving.
The overall net migration figure is still well short of the government’s target to reduce net migration to below 100,000, a pledge made in the 2010, 2015 and 2017 Tory manifestos.