The vote, which echoes the rise of populism in Europe and the United States, will shape the future of Europe. A victory for "out" could unleash turmoil on financial markets.
"It's very close; nobody knows what's going to happen," Prime Minister David Cameron told Wednesday's Financial Times, with opinion polls showing the rival camps neck and neck.
Thursday's vote will take place a week after the murder of ardently pro-EU lawmaker Jo Cox shocked the country, raising questions about the tone of an increasingly bitter campaign.
Much of the debate has boiled down to two issues: the economy and immigration.
The City of London, the International Monetary Fund and the majority of British business leaders back Cameron and his Remain camp's stance that to leave the EU would plunge Britain into recession, costing jobs and raising prices.
Those supporting a "Brexit" have struck a chord with many voters by saying Britain would regain control of immigration if it cut itself loose from a bloc they regard as domineering and out of touch.
Both camps have been accused of using unfounded assertions and scare tactics.
In one of the last debates, London's newly elected mayor, Sadiq Khan, accused Boris Johnson, the main leader of the Leave campaign, of exploiting fears of immigration to stoke anti-EU opinions.
"Your campaign hasn't been 'project fear', it's been 'project hate' as far as immigration is concerned," Khan said to huge applause from the 6,000 crowd at a live TV debate at London's Wembley Arena on Tuesday night.
Johnson, favorite with bookmakers to replace Cameron if Leave wins, told the cheering audience: "This Thursday can be our country's independence day."
Johnson, Khan's Conservative predecessor as mayor of London, said the Remain camp spoke of nothing but fear and was "rubbishing" Britain. He planned to travel across Britain in a helicopter on Wednesday to try to mobilize voters.
Opinion polls have painted a contradictory picture of public opinion in a deeply divided nation. But some published since Cox's murder have suggested a slight lead for Remain, though often within the margin of error.
A man accused of her murder gave his name as "death to traitors, freedom for Britain" when he appeared in court on Saturday. Cox's husband said on Tuesday his wife had been killed because of her strong political views.
The implied probability of a Remain vote was at 76 percent, according to Betfair odds, while the pound edged back to $1.4659 after climbing to as high as $1.4788 on Tuesday, its highest level since Jan. 4.
Polling stations open at 0600 GMT on Thursday June 23 and close at 2100 GMT. The official result is due some time after 0600 GMT on Friday but partial results and turnout figures from 382 counting centers will be announced from about 0100 GMT.
World leaders including U.S. President Barack Obama, Chinese President Xi Jinping, German Chancellor Angela Merkel and the NATO and Commonwealth allies have urged Britain to remain in the EU. Some have warned of the drawbacks of isolation.
France's government spokesman said on Wednesday Britain would lose access to the EU's prized single market if it voted to quit and ceased paying into the common budget.
Brexit?
Cameron, who called the referendum under pressure in his own Conservative party and from the insurgent anti-EU UK Independence Party, urged voters to remain in the club Britain joined in 1973.
"If we leave we will diminish our country and our ability to get things done in the world," he told supporters in Bristol in western England.
"We've got one day left to hammer out that message; stronger, safer, better off. Please give it everything you've got in these last hours to make sure that people go out and vote tomorrow."
The prime minister's fate hangs on the result. A vote to leave would almost certainly lead to his exit from the top job, though he has said he will stay. But even a narrow vote to remain could undermine his authority and shorten his term.
The bosses of 51 of the FTSE 100 British companies, and 1,285 business leaders who together employ 1.75 million people, signed a joint letter to The Times urging voters to remain.
"Britain leaving the EU would mean uncertainty for our firms, less trade with Europe and fewer jobs," they said. "Britain remaining in the EU would mean the opposite: more certainty, more trade and more jobs."
A vote to leave could unleash turmoil on foreign exchange, equity and bond markets, lead to a political crisis in Britain and fragment the post-Cold War European order.
London-based money transfer website Transferwise said it was suspending pound transfers on Thursday in anticipation of currency volatility.
The EU would have to weather the exit of its No.2 economy representing $2.9 trillion of its gross domestic product, the only European financial capital to rival New York and one of its only two nuclear powers, while Britain's economy could stall.
A vote to remain would trigger a rise in sterling and relief in Western capitals, unleash pent-up investment in Britain but still leave the country -- and the Conservatives -- bitterly divided, especially if the margin of victory were thin.
Investment bank Citi estimated in a research note there was a 60 percent chance Britons would vote to stay in the EU but said a "close remain" could still undermine political stability in both the United Kingdom and the 28-country bloc.
"A vote to 'Leave' would have major repercussions in global financial markets, the economy and politics, triggering substantial downward revisions of UK and European growth forecasts," Citi said.
Meanwhile, bookmaker William Hill said about 20 million pounds had been staked on the outcome of the referendum across the industry, with two-thirds of the money staked on a vote to remain in the EU.
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