Nigel Farage emerged as the winner from a head-to-head debate with Nick Clegg over Britain's future in the European Union, an instant poll indicated.
Some 57% of those surveyed thought Ukip leader Mr Farage had performed best, compared to just 36% for the Deputy Prime Minister.
The YouGov poll of 1,003 people followed the debate hosted by LBC radio and televised live by news channels in which Mr Farage said it was time to leave the European Union, calling it a "failed project".
But Liberal Democrat leader Mr Clegg insisted: "We are better off in Europe - richer, stronger, safer - and that's why I will fight to keep us in, for the sake of jobs, for the sake of our clout in the world, for the sake of Britain."
The UK Independence Party leader and Deputy Prime Minister went head-to-head in the first of a series of two EU debates which have been billed as pitching the party of in against the party of out. Neither Prime Minister David Cameron nor Labour leader Ed Miliband took part in the event in London, less than two months ahead of the May 22 elections to the European Parliament.
Following the clash, bookmakers Ladbrokes cut the odds on Ukip securing the most votes in the Euro-election from 6/4 to 11/10, making them joint favourites with Labour.
The pair traded statistics on the potential impact on jobs and growth of EU exit, and each accused the other of distorting figures to support their case.
At one point, Mr Clegg brandished a Ukip by-election leaflet which claimed that 29 million Romanians and Bulgarians might come to the UK due to EU freedom of movement laws, telling him: "There aren't even 29 million Romanians and Bulgarians living in Romania and Bulgaria."
Mr Farage accused the Lib Dem leader of misleadingly suggesting that three million jobs could be at risk if Britain left the EU, insisting that the figure referred only to jobs that were linked to European trade, not those which were under threat.
At one point, Mr Clegg questioned the Ukip leader's patriotism over the extradition of crime suspects who flee abroad, while he also suggested that Ukip wanted to "turn the clock back" to the 1950s by taking Britain out of the 28-nation EU bloc within which it currently does trade deals with the rest of the world.
Mr Farage retorted: "People like Nick don't think Britain is good enough. We are just not good enough, we must give away control of all of these things to somebody else who will do it for us. We are too small to survive."
In an ironic echo of David Cameron and Gordon Brown's comment "I agree with Nick" in the 2010 leaders' debates, the Ukip leader told moderator Nick Ferrari: "By the way, I don't agree with Nick."
After winning the toss of a pound coin, Mr Farage invited the Liberal Democrat leader to "open the batting", and Mr Clegg made a brief opening address, staring straight into the TV camera as he did in the 2010 leaders' debates.
"Make no mistake - if we cut ourselves off from Europe, from the countries that we trade with more than anyone else, then our hard-won economic recovery will simply be thrown away," said Mr Clegg.
He said he wanted "a Britain that leads in the world by standing tall in our own European backyard".
But Mr Farage retorted: "This debate is between a tired status quo defending a crumbling EU that frankly isn't working any more, and a fresh approach that says let's be friendly with Europe, let's trade with Europe, but let's not be governed by their institutions."
Despite Mr Cameron's promise of an in/out referendum by the end of 2017, and Labour and Lib Dem pledges of a public poll if more powers are transferred to Brussels, Mr Farage said that all three parties would " do their absolute best" not to put the issue to a vote.
Calling for a referendum before next year's general election, the Ukip leader asked: "Why don't we trust the British people to make their minds up on what I think is the most important constitutional question we have faced in this country for 300 years: are we to be a self-governing nation or not?"
He denied that a vote for Ukip would make a plebiscite less likely, insisting that only one-third of Ukip's support comes from the Conservatives, with the rest from Labour and people who had stopped voting.
Mr Clegg said a referendum now, with the EU in "a real state of change and flux" would mean "I don't think we would really know what we were having a referendum on".
On immigration, the Lib Dem leader claimed the NHS would "collapse" without foreign workers and insisted that "p eople who come to our country, they create wealth, they pay taxes, they help sustain our NHS". Pulling up the drawbridge would "de stroy jobs for everybody in this country", he said.
Mr Farage said Mr Clegg had failed to acknowledge that the UK had a "total open door to 485 million people from Europe, many of them from poor countries".
He added: "That is the issue that has woken people up, that by being a member of the European Union we have lost the ability to govern our country and to control our borders."
Mr Clegg warned that multi-national companies would pull jobs and investment out of the UK if it left the EU, citing comments from companies like Siemens, Nissan and Ford.
"That would be devastating for the UK economy," said Mr Clegg. "T hey will exit the UK, leaving thousands and thousands of families distressed in their wake because they will not have a breadwinner in those families, able to pay their bills, because the investment has gone, the jobs are gone.".
But Mr Farage said: "I remember, Nick, you and all your gang - all the big corporates - all telling us 12 years ago that if we didn't join the euro, all inward investment would cease, the City of London would disappear.
"All I can say is thank God we didn't listen to you, otherwise we would have been in one hell of a mess."
The Ukip leader said the UK was now "the eurozone's biggest export market in the world" and would hold "the whip hand" in obtaining good terms in any trade negotiations following exit.
Responding to the Ukip leader's taunts that he had never had "a proper job in the real world", Mr Clegg said: "Nigel Farage and I were elected to the European Parliament on the same day in 2009. I left the European Parliament after five years. He still remains a euro-politician."
Recalling the use of the European Arrest Warrant to bring back 21/7 bomber Hussain Osman and teacher Jeremy Forrest, who took a schoolgirl to France, to face justice in the UK, Mr Clegg asked: "How on Earth is it possible for Ukip to claim it is somehow patriotic to make our streets less safe, how on Earth is it possible for you to say you would stand up for Britain if you would not actually extradite and bring back hundreds of people to face British justice?"
But a visibly angry Mr Farage said that the arrest warrant had allowed a London man to be left "to rot in a Greek hellhole for over a year without his rights of habeus corpus". He said: "I think it's an abomination. How you can call yourself a liberal and support the destruction of all the great principles of British liberty by signing up to European law I do not know."
Mr Clegg challenged Mr Farage over his claim that 75% of the country's laws were derived from Europe, saying the House of Commons library had put the figure at roughly 7%.
Asked where the 75% figure had come from, Mr Farage said: "That's the estimate that we have made."
He said the UK and the other northern European countries played by the rules but "in the south they have a completely different attitute".
In his closing statement Mr Clegg urged voters of other parties who supported remaining in the EU to back the Lib Dems in May's European elections.
"I want us to be Great Britain, not little England and if you feel the same then now is the time to make your voice heard because Labour and the Conservatives are going to do nothing to stop us heading towards the exit," he said,
Mr Farage said: "Nick represents a tired status quo, defending a model that maybe 40 years ago looked like a good idea but leaves us totally unfit to compete in the 21st century global economy."
After the debate the Ukip leader said he had enjoyed the experience, but had found Mr Clegg "very evasive" on the immigration issue.
Audience member Varsha Nursimloo, 24, a Labour supporter from London, thought Nigel Farage won the debate, even if he didn't win her over.
"It was very close but Nigel Farage was the winner in my eyes," said the marketing executive. "His facts probably weren't quite correct but I think he had an answer for a lot of things."