By Guy Faulconbridge, Michael Holden and David Milliken

LONDON (Reuters) - British Prime Minister David Cameron and his eurosceptic opponents made final pitches for wavering voters on Wednesday on the eve of a defining referendum on European Union membership with the outcome still too close to call.

The vote, which echoes the rise of populism elsewhere in Europe and the United States, will shape the continent's future. A victory for "out" could unleash turmoil on financial markets and foreign exchange bureaux reported a surge in demand for foreign currency from Britons wary sterling may fall.

"Quitting Europe is a risk to your family's future because a vote to leave on Thursday means there is no going back on Friday," Cameron said.

Some voters appeared to be heeding his message as three of four polls released on Wednesday showing a move toward staying in the EU. Two still showed a lead for "Leave", while the other two showed a lead for "Remain".

Most pollsters said the result was too close to predict, and would depend on turnout on the day and any late swing among the substantial number of undecided voters.

"It's our last chance to sort this out and take back control," said former London mayor Boris Johnson, the main leader of the Leave campaign and favorite with bookmakers to replace Cameron in the event of Brexit.

Polling company ComRes said "Remain" now looked likely to win after it reported a 6 percentage point lead in a survey for the Daily Mail and broadcaster ITV.

"The burning question now is whether Remain's win will be of a sufficient margin to settle the issue of EU membership for a generation, as David Cameron put it," ComRes chairman Andrew Hawkins said.

Sterling surged to its highest so far this year against the dollar after the ComRes poll, and online betting market Betfair priced in an 80 percent chance Britain would stay in the EU.

Cameron has promised further reform if Britain stays in the EU, but European Commission chief Jean-Claude Juncker warned there would be no further renegotiation whatever the result on Thursday, after EU leaders reached a deal on a new settlement for Britain in February.

French President Francois Hollande said a vote to leave could seriously jeopardize British access to the EU's prized single market.

German Chancellor Angela Merkel said she did not want to speculate on what dangers would arise if Britain left, because she wanted it to stay in the Union.

The referendum will take place a week after the murder of pro-EU lawmaker Jo Cox shocked the country, raising questions about the tone of an increasingly bitter four-month campaign.

Much of the debate has boiled down to two issues: the economy and immigration.

The City of London financial center, 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.

Supporters of a so-called 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 see as domineering and out of touch.

In what has become an ugly and personal fight, both camps have been accused of using unfounded assertions and scare tactics. Remain campaigners accuse their opponents of resorting to the politics of hate; the Leave camp say their rivals have run a "Project Fear" to scare voters about the economic risks.

Both sides hit the road and the airwaves to appeal to the large number of undecided voters who will be decisive, along with the level of turnout.

"INDEPENDENCE DAY"

Johnson was flying around Britain in a helicopter to spread the Brexit message, making an unashamed play to British patriotism by declaring Thursday could be "independence day".

The leader of the anti-EU UK Independence Party (UKIP), Nigel Farage, also played the nationalist card in an address to supporters in London.

"At the end of the day tomorrow when people vote they must make a decision - which flag is theirs? I want us to live under British passports and under the British flag," he said.

Cameron, who called the referendum under pressure from his own Conservative party and from the insurgent UKIP, urged voters to remain in the club Britain joined in 1973, telling a crowd in Bristol in western England leaving would "diminish" the country.

Standing alongside him, former Prime Minister John Major said the result would have to be respected but warned that if Leave won, "the gravediggers of our prosperity will have to account for what they have said and done".

Opinion polls have depicted a deeply divided nation, with big differences between pro-EU London and Scotland and eurosceptic Middle England.

Election experts say turnout will be crucial because of another gulf, between generations. Young people, who have a poor voting record, strongly back staying in the EU, while elderly, more regular voters tend to favor an exit.

Opposition Labour Party supporters are seen as being more pro-EU than Conservatives, but less passionate about the issue.

Labour leader Jeremy Corbyn, who voted "No" in a previous 1975 referendum on staying in the European Economic Community, and who has been criticized for lukewarm backing for the Remain cause, attempted to galvanize his party on Wednesday.

"Vote for jobs, vote for rights at work, vote for our NHS (National Health Service), vote to remain in the European Union," he told a rally in London.

Bond trading giant PIMCO's head of sterling portfolios said the pound could fall to $1.30, its lowest level against the dollar in 30 years, if Britons vote for Brexit.

Polling stations open at 0600 GMT on Thursday June 23 and close at 2100 GMT with 46.5 million electors eligible to vote. 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 and NATO and Commonwealth allies have urged Britain to remain in the EU.

BREXIT?

Cameron's personal future also hangs on the result. The EU issue has divided his Conservative Party since the days of his distant predecessor Margaret Thatcher, bringing an end to her decade in office in 1990.

A vote to leave would almost certainly cost him the top job, though he has said he will stay. But even narrow backing for remain could undermine his authority and shorten his term.

A Brexit vote could also lead to a wider political crisis in Britain and fragment the post-Cold War European order.

EU leaders, while unanimously urging Britain to stay, are already skirmishing over whether the right response to a Brexit would be closer integration of the remaining members or a rethink of the way Europe is governed.

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.

Scotland's First Minister has said Brexit could also trigger another independence referendum if Scots backed staying the EU but were dragged out by the English.

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.

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.

"It would see the UK stay in the EU, but could trigger domestic political risks, such as the PM's resignation and potentially a constitutional crisis, with parts of the UK voting Leave and others Remain," Citi said.

(Additional reporting by Kylie MacLellan, Andy Bruce, Kate Holton and David Miliken; writing by Guy Faulconbridge; editing by Paul Taylor, Timothy Heritage and Philippa Fletcher)