David Cameron, Ed Miliband and Nick Clegg have an uphill struggle before any EU referendum according to a poll that says only one in three would vote to stay in the bloc.
The findings, which are likely to spark alarm in pro-European circles, suggest that anti-Brussels sentiment is sweeping through the British public.
Given an in-out referendum on EU membership tomorrow, 50 percent would vote "out" against 33 percent "in" and 17 percent who would not vote either way, according to the poll by Harris Interactive for the Financial Times.
Mr Cameron, who had resisted calls to hold a referendum, finally bowed to pressure last month by promising that a Tory government would do so in 2017.
The Conservative leader said if his party won the next election he would seek to repatriate various powers from Brussels before putting EU membership to the public.
The prime minister, who would campaign for an "in" vote, said he had "no illusions about the scale of the task ahead", a comment borne out by the Harris poll of 2,114 adults, conducted between January 29 and February 6.
The promise of a plebiscite is very popular with the electorate, with 50 percent supporting the decision and only 21 percent opposing it.
Mr Cameron has delighted his backbenchers with the move, designed in part to stave off a potential electoral threat from a resurgent UK Independence party.
It would be the first national referendum on Europe since 1975 when Harold Wilson, the Labour prime minister, put membership of the European Economic Community to the public.
But Mr Cameron has also stoked nervousness in Paris, Berlin and Washington from allies concerned about the risk of a Tory government accidentally finding itself outside the EU.
The prime minister believes that he will be able to convince the public of the merits of staying in the EU so long as he can renegotiate the relationship.
Yet of those who would vote "out", only 12 percent said they would "definitely" change their minds if there was a successful renegotiation. Another 47 percent said "yes, possibly" to the idea that they could alter their vote. But 41 percent of those wanting Britain to leave would definitely not change their point of view.