LONDON (AFP) - Prime Minister David Cameron invoked Britain's wartime spirit in a last-ditch bid to win votes on Wednesday on the eve of a knife-edge referendum on European Union membership that has put the continent on alert.

"Winston Churchill didn't give up on European democracy... and we shouldn't walk away," David Cameron told a crowd in Birmingham, his final rally in a campaign that has been described as one of Britain's most bitter ever.

EU leaders warned that leaving the 28-member bloc would be final, as two polls indicated the "Leave" camp was just ahead of "Remain".

"If you jump out of the airplane, you cannot clamber back through the cockpit hatch," Cameron warned, his sleeves rolled up and pointing for emphasis.

"Put your children's future first." As planes with banners from the rival campaigns flew over London to woo the undecided, two polls showed the "Leave" side with the slimmest of leads, both within the margin of error.

"Our latest poll suggests that Leave is in a stronger position than Remain," said Luke Taylor of TNS, after their poll put "Leave" on 43 percent and "Remain" on 41 percent.

Record numbers of voters have registered for the ballot, and Taylor emphasised the result could all come down to turnout.

A Brexit vote would mean Britain would be the first country to leave the European Union in the bloc's 60-year history, leaving it in uncharted waters at an already troubled time.

"Out is out," European Commission chief Jean-Claude Juncker said in Brussels, dismissing any talk of a post-vote renegotiation just hours before polls open.

French President Francois Hollande warned an exit would be "irreversible" while German Chancellor Angela Merkel said she wanted Britain to stay but that the decision was down to the British people.

The German and French leaders will meet in Berlin next week for talks Hollande said would work "towards relaunching the European project", already struggling with an unprecedented migrant crisis.

Cameron's main rival in the "Leave" campaign and possible successor, Boris Johnson, said Britain stood on the brink of "independence day" from Europe.

"I do think that we are on the verge, possibly, of an extraordinary event in the history of our country and indeed in the whole of Europe," Johnson said in eastern England.

Nigel Farage, leader of the anti-EU UK Independence Party, said: "I genuinely believe we are going to win this." US Republican White House hopeful Donald Trump, who arrives in Britain Thursday, also spoke out on Brexit again, saying he thought the country should "go it alone".

A British withdrawal would trigger a lengthy exit negotiation, leading to the loss of unfettered access to its partners in the 28-nation market and forcing the country to strike its own trade accords across the world.

In Europe, the referendum has raised concerns of a domino effect of exit votes that would imperil the integrity of the bloc, already buffeted by the eurozone and migration crises.

Though many voters fret over the financial consequences of a Brexit, others relish the prospect of taking back power from Brussels and reining in high levels of immigration.

"I think we need to make our contribution to Europe and to the global economy. And the best way we can do that is by being in it," Chet Patel, a 44-year-old telecoms worker told AFP.

Pat Hand, a 50-year-old construction worker, said he would be voting to leave the EU. "The country is in an absolute mess," he added.

Momentum for the "Leave" campaign, however, appeared to be upended with last week's killing of pro-EU lawmaker Jo Cox of the main opposition Labour party, which prompted concerns the campaign had been divisive.

"Jo's killing was political. It was an act of terror," Cox's husband Brendan told thousands of mourners who gathered in London's Trafalgar Square to mark what would have been her 42nd birthday.

Pakistani Nobel Peace Prize winner Malala Yousafzai, who survived an assassination attempt by Taliban extremists for advocating education for girls, told the crowd: "I'm here today as a living proof that they can't win with bullets." A floral tribute to Cox was also towed along the River Thames to a mooring outside the Houses of Parliament.

Though the polls show the race is virtually neck and neck, bookmaker Betfair said their latest odds implied a 76-percent chance of "Remain" winning.

In the latest surveys released, Opinium put the "Leave" camp at 45 percent and "Remain" at 44 percent, while TNS gave them a lead of 43 percent to 41 percent for staying.

With everything to play for, a string of prominent figures rolled out last-minute endorsements.

James Bond star Daniel Craig and Irish rock band U2 endorsed "Remain", while bosses from nearly 1,300 of Britain's leading businesses warning in the Times that Brexit would endanger jobs.