* Cameron set to deliver major speech on UK's EU future
* Poll puts Cameron's party behind anti-EU party
* Eurosceptics want "in or out" referendum on EU
* Pro-Europeans warn of investment risk
By Michael Holden
LONDON, Jan 13 (Reuters) - European Union supporters and opponents turned up the pressure on British Prime Minister David Cameron on Sunday as a poll showed most Britons wanted a referendum on Britain's membership of the EU although the number supporting withdrawal had fallen.
Cameron is expected to deliver a major speech this month in which he will set out plans to renegotiate Britain's position within the 27-member EU, along with the terms of a historic vote on the subject that could help define Britain's role in international affairs for decades.
Many lawmakers in his own Conservative Party are pressuring him to call a full-fledged referendum on whether Britain should remain in the EU, and growing support for the anti-European party UKIP at the expense of the Conservatives has fuelled their demands.
Meanwhile, pro-European Conservatives and business leaders are also becoming more vocal in trying to stop Cameron stepping back from the bloc, saying a radical downgrade of ties with Britain's biggest trading partner would drive away investment.
According to a ComRes poll in the Sunday People newspaper, UKIP, which wants Britain to exit the EU and has never won a seat in the Westminster parliament, is on course to push the Conservatives into third place in next year's elections for the European Parliament.
The survey found 35 percent of Britons would vote for the opposition Labour Party, 23 percent for UKIP, and just 22 percent for the Conservatives. Support for the pro-European Liberal Democrats, the junior partner in Cameron's coalition government, was down to 8 percent.
The poll also showed that although a clear majority backed having a referendum on whether Britain should remain in the EU, support for such an "in or out" vote had fallen by 5 points to 63 percent since the last such ComRes survey in October 2011.
The number who would vote for outright withdrawal also dropped from 37 percent to 33 percent, while the number who would oppose such a move rose 5 points to 42 percent.
The findings come after a week when international partners from the United States to Germany and Ireland have made it clear they oppose a British EU exit and believe that such a move would isolate and damage Britain itself.
The issue dominated British Sunday newspapers as those on both sides of the argument sought to get their message across.
According to the papers, a group of eurosceptic Conservative lawmakers, called "Fresh Start", would this week demand radical repatriation of powers, saying Britain should take unilateral action and break treaty obligations if necessary.
On the other hand, the Observer reported that an alliance of senior cross-party figures were to unite to spearhead the "Centre for British Influence through Europe", a group that would fight moves to pull Britain back from the EU.
The exact detail of what Cameron's will say remains unclear. The Mail on Sunday's front page, without citing any sources, said the prime minister thought it would be mad for Britain to leave the bloc and was "secretly" backing those who said it would damage Britain economically and diplomatically.
However, the Independent on Sunday said Cameron, who is keenly aware that eurosceptics in his party helped to bring down the Conservatives' last two prime ministers, Margaret Thatcher and John Major, was sympathetic to some of the Fresh Start group's ambitions for renegotiating powers.
Labour leader Ed Miliband said Cameron's approach of trying to appease both sides was "incredibly dangerous".
"I think he is essentially sleepwalking us towards the exit door from the European Union," he told BBC TV.