Counting is expected to continue into Friday morning, according to reports.
Opinion polls conducted in days leading up to Thursday's referendum vote showed the British public evenly split.
Those advocating exiting the EU argue it will allow Britain to take back control of its borders and that it could help Britain's economy, already strong as the fifth largest in the world, to expand without having to adhere to the numerous rules on business and charges in EU membership fees.
Many economic experts in the United States warn that if Britain exits the EU, the uncertainty of the global financial impact could send stocks diving.
Britain last voted on whether to remain in the EU, an economic and political partnership made up of 28 European countries, in 1975.
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