The Opinium/Observer survey finds that 56% of people would probably or definitely vote for the UK to go it alone if they were offered the choice in a referendum. About 68% of Conservative voters want to leave the EU, against 24% who want to remain; 44% of Labour voters would probably choose to get out, against 39% who would back staying in, while some 39% of Liberal Democrats would probably or definitely vote to get out, compared with 47% who would prefer to remain in the EU.
The findings will make sobering reading for all three major parties, which are at risk of losing support to the buoyant anti-EU party Ukip – now two points ahead of the Lib Dems on 10%.
Overall just 28% of likely voters think the EU is a "good thing" while 45% think it is a "bad thing". The 18-34 age group is the only one in which there is a clear majority backing the EU, with 44% saying membership is good, against 25%.
The poll will pile yet more pressure on David Cameron to negotiate a tough deal on the EU budget as he prepares for a Brussels summit, beginning on Thursday, at which EU leaders will attempt to hammer out a financial deal for the union for the seven years from 2014.
The prime minister's problems deepened on Saturday when one of the ringleaders of a recent Commons rebellion on EU financing, the Eurosceptic MP Mark Reckless, predicted an even bigger revolt if Cameron returned from Brussels without having negotiated a real-terms cut in EU spending, or wielded a veto.
He added that if Labour, which joined the rebels in calling for an actual cut in the budget, stood firm then Cameron would be defeated. "He is between a rock and a hard place," said Reckless.
Cameron had wanted to go to Brussels arguing for a freeze in EU spending – a negotiating position he believed would attract support from other net contributing nations including Germany and the Netherlands. But having had his hand forced, he is now under pressure to go for an actual reduction – a position that no other EU nation is likely to support.
On Monday Ed Miliband will make a keynote speech to the CBI in which he will argue that every effort should be made to prevent the Tories leading the country towards the EU exit door. He will also say that under the Tories, Britain is "sleepwalking towards exit" from the EU. Labour pro-Europeans accused Cameron of lurching further to the right as it was confirmed Boris Johnson's former election guru, the Australian Lynton Crosby, has become the prime minister's general election strategist.
The poll, which showed Labour's lead over the Tories has dropped from 11% two weeks ago to 7% now, with the Lib Dems on 8% and Ukip on 10%, found that voters over 55 were the most critical of the EU, with 59% saying it was a bad thing and 20% a good thing.
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