The Office for National Statistics said net migration to Britain from the EU, those arriving in Britain minus those leaving, hit 189,000, up from 180,000 during the previous year.
Overall net migration to Britain was estimated to be 335,000, just 1,000 short of the record high reached in the same period last year.
Prime Minister Theresa May has promised to control immigration.
Net migration from EU to Britain hit record high ahead of EU vote
01 December 2016
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Net migration from the EU to Britain hit a record high in the year to June 2016, according to official data for the twelve months before the EU referendum in which concern about rising immigration drove much opposition to the bloc.
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