By Costas Pitas

LONDON (Reuters) - Net migration from the European Union to Britain hit a record high in the 12 months running up to June's referendum vote to leave the bloc, in which concerns about immigration motivated many Brexit voters.

The ruling Conservatives had promised to cut annual immigration to under 100,000 but have failed to fulfill their pledge partly as the number of European new arrivals continued to rise, spurred on by factors such as better job prospects.

Net migration to Britain from the EU, those arriving minus those leaving, reached a new record of 189,000 in the year to June, the Office for National Statistics (ONS) said. Overall net migration was 335,000, just 1,000 short of the previous high.

Prime Minister Theresa May has promised to control immigration as part of a Brexit deal, with many voters blaming the EU's freedom of movement rules for the increase in new arrivals which the government said it may now be able to limit.

"Brexit gives us the opportunity to be able to control numbers coming in from Europe," immigration minister Robert Goodwill told Sky News on Thursday.

"We want to return to sustainable levels and that's all about... the pressure it puts on the health service, the pressure it puts on education, the pressure it puts on housing and that was very clear during the referendum," he said.

Britain has yet to detail its aims ahead of EU divorce talks but many European leaders have already said it should not expect to keep unfettered access to the single market, key to many businesses, and be able to limit freedom of movement at the same time.

Just over half of net migration to Britain came from non-EU nations but Romania became the most common country of last residence for immigrants arriving in Britain in 2015, accounting for 10 percent of all new arrivals, the ONS said.

Until 2013, Romanians and Bulgarians had been limited in the types of work they could do in Britain.

The presence of large minority communities and the English language have long made Britain an attractive place but high unemployment and lower wages in southern Europe have helped spur on recent waves of immigration.

Employment opportunity was the key factor, according to the ONS' Head of International Statistics Nicola White.

"The main reason people are coming to the UK is for work, and there has been a significant increase in people looking for work, particularly from the EU," she said.

(Editing by Catherine Evans and Stephen Addison)