By Michael Holden and Kylie MacLellan

LONDON (Reuters) - Lawmaker Jo Cox, who was shot and stabbed a week before Britain's referendum on European Union membership, died because of her political views and had been deeply troubled by the tone of the campaign, her husband said on Tuesday.

Prime Minister David Cameron appealed to voters across the generation gap to back staying in the EU, two days before a closely fought referendum that will shape the future of Europe. The campaign to leave the EU has echoes of populist movements across Europe and in the United States.

The murder of Cox, a 41-year-old mother of two young children who was an ardent supporter of EU membership, shocked the country and abruptly changed the tone of a caustic campaign that has polarized Britons.

"She had very strong political views and I believe she was killed because of those views," her husband Brendan Cox told broadcasters. "She died because of them and she would want to stand up for those in death as much as she did in life."

It was unclear how Brendan Cox's words might influence the EU vote that Cameron said was likely to be "very close".

Cox had been worried about Britain's political culture, including a coarsening of language and people taking more extreme positions, her husband said. She was also concerned about divisive politics globally.

"She worried about the tone of the debate" that focused increasingly on immigration and "about the tone of whipping up fears and whipping up hatred".

"I think the EU referendum has created a heightened environment for it but actually it also pre-existed that," he said.

Britons vote on Thursday on whether to quit the 28-nation bloc amid warnings from world leaders, investors and companies that a decision to leave would diminish Britain's influence and unleash turmoil on markets.

In an interview with the Financial Times, Cameron also predicted a "remain dividend" in the form of an investment surge if Britons voted to stay in the 28-nation bloc.

'BRITS DON'T QUIT'

In an earlier address outside his Downing Street office, Cameron hammered home his message that leaving the EU would jeopardize Britain's economy and its national security, with fewer jobs, fewer allies and higher prices.

"Brits don't quit," he said, using the official backdrop to make a direct pitch to older voters considered more eurosceptic and more likely to vote.

"It will just be you in that polling booth. Just you, taking a decision that will affect your future, your children's future, your grandchildren's future."

The Conservative prime minister's remarks came as an opinion poll showed very narrow support for staying in the EU. The Survation poll put the "Remain" camp just one percentage point ahead of the campaign for a so-called Brexit, well within the margin of error.

Opponents said Cameron's appearance suggested he was worried about the outcome.

As each side sought to play its last trump cards, the pro-EU "Britain Stronger in Europe" campaign issued a final poster of a door leading into a dark void with the slogan: "Leave and there's no going back."

If Britain votes to leave, Cameron would face pressure to resign, though he has said he will continue as leader.

Campaigning was suspended for three days after Cox's killing in northern England last Thursday.

Some Leave campaigners accuse the Remain camp of exploiting her death.

After Cox's killing, opinion polls indicated sentiment had swung back to the Remain side after a shift toward Leave.

An earlier ORB survey for the Daily Telegraph put support for Remain at 53 percent, up 5 percentage points on the previous one, with Leave on 46 percent, down three points.

"QUEEN IS ABOVE POLITICS"

Former England soccer captain David Beckham, a popular public figure, added his voice to Remain's list of celebrity supporters. "For our children and their children we should be facing the problems of the world together and not alone," he said.

Leave campaigners stepped up their focus on what they call uncontrolled immigration, saying Cameron had been warned four years ago his goal of reducing net arrivals was impossible due to EU rules.

The anti-EU UK Independence Party issued a poster showing a traffic jam with the message "The school over-run" and saying nearly one in four of Britain's primary schools were full or oversubscribed.

The Leave camp says it is the anti-establishment choice, and its message that EU membership has handed political control to Brussels and fueled mass immigration has struck a chord with many Britons.

Already shaken by differences over migration and the future of the euro zone, the EU would lose its second-largest economy, one of its top two military powers and by far its richest financial center.

Britain's Daily Mail newspaper came out for the Leave campaign, while the Daily Mirror endorsed Remain.

The Sun, Britain's biggest-selling newspaper, which came out for "Leave" last week, said in its Wednesday edition the queen asked guests at a private dinner: "Give me three good reasons why Britain should be part of Europe," suggesting she may favor Brexit.

"The Queen is above politics and acts on the advice of Her Government in political matters. The referendum is a matter for the British people to decide," Buckingham Palace said in a statement.

(Additional reporting by Elisabeth O'Leary, John Geddie, Kate Holton, Estelle Shirbon and James Davey; Editing by Janet McBride and Cynthia Osterman)