Voter participation was reported to be "very high" Thursday in Britain's EU membership referendum as counting got underway across the country.

Turnout for the historic poll was estimated by Sky News to be 83.7 percent - which, if confirmed, would be the most popular nationwide election in the U.K. for more than half a century.

With the first results expected at midnight local time (2300GMT), new opinion polls suggested a narrow win for the Remain campaign.

An analysis by pollsters Ipsos Mori conducted Wednesday and Thursday gave a 54 percent to 46 percent lead for Remain over Leave.

Shortly after voting ended at 10 p.m. local time (2100GMT), Prime Minister David Cameron tweeted: "Thank you everyone who voted to keep Britain stronger, safer & better off in Europe - and thousands of @StrongerIn campaigners around the UK."

Former Mayor of London Boris Johnson, a leading campaigner for Brexit, said "democracy has been served" in a short message of thanks, while U.K. Independence Party Nigel Farage told Sky News that it "looks like Remain will edge it."

Once the result becomes clear Friday morning, attention is expected to turn to the state of Britain's governing Conservative Party, whose members have been deeply divided by the referendum campaign.

A letter from 84 Conservative lawmakers delivered to Cameron on Thursday evening urged him to remain in office even if the referendum produces a Leave result.