Two-thirds of people believe the multi-billion annual cost of EU membership is too high and does not represent value for money, the survey found.
Regaining control over UK borders to end mass migration from other EU nations was widely seen as the top priority for voters.
And an overwhelming majority wanted a far bigger reduction in meddling from Brussels than David Cameron is seeking in his diplomatic push for a new EU deal for Britain, the figures showed.
Eurosceptics seized on the findings as clear evidence that the campaign for a British exit is winnable when the forthcoming in-or-out referendum on the country's EU membership is held.
Ukip leader Nigel Farage said: "The ‘No to EU’ side can win this referendum as long as we make the right arguments on the issues people really care about such as border controls, which is exactly what we in Ukip intend to do."
The survey of 5,000 voters by polling firm Survation, commissioned by the Alliance for Direct Democracy in Europe, is the biggest detailed study of public opinion on Europe for years.
It asked a series of questions about attitudes to the EU and what should be the Prime Minister's top priorities in his drive to renegotiate the country's EU membership deal.
Immigration was seen as the most important issue in his diplomatic push, according to the poll.
Thirty-two per cent of voters stated that "ending the free movement of people" across EU borders should be the top item on his agenda in his diplomatic push.
A further 18 per cent wanted the restoration of sovereignty from Brussels to the Westminster parliament as the top priority.
And 15 per cent wanted the cost of EU membership, currently around £11billion a year, slashed so the cash could be spent within the UK
Mr Farage pointed out that the top three priorities for EU reform were not even on Mr Cameron's shopping list.
He said: "It is clear that Cameron's so-called renegotiation is a farce, given he has no intention of fighting for the changes the British people want.
"Open-door immigration, even to those currently undecided about whether to remain in the EU or not, is the number one concern. David Cameron has no intention of addressing this.
"It is vital therefore that EU open borders are part of this referendum debate.
"The fact that inside the EU we have no say over the quantity nor quality control of those who come to our country is of huge significance to the British people and we must highlight that we can only control the numbers coming in by voting No and leaving the EU.
"It is also clear that the British people want a Parliament which is free to make it's own laws without interference from the EU and to stop money flowing from the UK to Brussels.
"None of these issues are even open for discussion and so we in Ukip will be campaigning hard to expose David Cameron's commitment to keep the UK locked inside the EU. Ukip will be leading the charge to secure a No vote."
The poll comes ahead of a new drive by Ukip to fire up the campaign for a British exit from the EU ahead of Mr Cameron's planned EU referendum.
The historic vote on the country's European future is due to be held by the end of 2017 but some Whitehall insiders believe it could come as early as June next year.
Earlier this week, the Prime Minister revealed that he is planning a fresh round of talks with German Chancellor Angela Merkel and other European leaders in his attempt to negotiate a new EU membership deal.
Ukip leader Mr Farage is planning to speak at dozens of public meetings around the country over the coming months to try to start winning the case for quitting the EU.
And in a major speech on Thursday he will say that time must not be wasted in the battle to win over voters.
According the Survation poll, the Yes to EU camp is currently ahead. It found that when voters who say they are likely to vote in the EU referendum were asked about their preference, 44.1 per cent supported staying in the EU while 35.7 per cent wanted to leave.
But senior Ukip figures believe the other poll findings confirm that feeling will shift drastically when the arguments are examined and the details of Mr Cameron's planned new EU membership deal are revealed.
According to the poll, only 37 per cent of those quizzed would vote to join the EU if the country was outside the bloc today.
Forty-two per cent of voters admitted to having no idea how much EU membership cost taxpayers while 66 per cent said the cost was too high and not value for money no matter what the actual cost was.
Forty-one per cent thought any savings if Britain does quit the EU should be spent on the NHS.
Nearly two thirds of voters (64 per cent) believed that the Westminster Parliament should be able to overrule EU law.
A Tory insider said: "The choice in the EU referendum should not be continued membership of the EU on the basis of the status quo but instead the British people should have the choice of a reformed relationship with the EU.
"Even though everyone said that it couldn’t be done, the British renegotiation’s been given the green light – kicking off a process to work through the substance and to find solutions.
"This will take us another step closer to addressing the concerns that people have about the EU.
"This will give the British people the choice of membership of a reformed European Union in an in/out referendum by the end of 2017.
"It will be for voters to decide whether to stay or leave."
The Daily Express has been at the forefront of the crusade for Britain to quit the EU for more than five years. Hundreds of thousands of readers backed a petition calling for a British exit from the union that was delivered to Downing Street. Express.
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