A record 284,000 EU citizens arrived in Britain in the year to June when the Brexit referendum was held, with a particularly high number coming from Romania and Bulgaria, official data showed on Thursday.
Net migration to Britain — the total of all migrant arrivals minus departures — was at a near-record of 335,000, far above the government's target of 100,000.
The period covered by the data goes to only a few days after the June 23 vote meaning it was "too early to say what effect, if any, the EU referendum has had," said Nicola White, head of international migration at the Office for National Statistics.
"Immigration levels are now among the highest estimates recorded," she said, adding that Romania was the most common country of previous residence in 2015, making up for 10% of the total.
May has also said she wants an "early agreement" to guarantee the status of the estimated three million EU citizens currently living in Britain once exit negotiations with the EU begin but will make this conditional on a deal for Britons living in the EU.
Today's data also showed a surge in citizenship applications by some of the EU nationals in Britain.
The number of outstanding applications from European citizens to secure residency in Britain rose to almost 100,000 in early July 2016 from 37,618 in June 2015, the Guardian newspaper reported.
Britons concerned about their ability live in other parts of the European Union after Brexit have meanwhile been applying for Irish citizenship.