Clegg, leader of the Europhile Liberal Democrats, yesterday argued that Britain was "better off in Europe - richer, stronger, safer", but UK Independence Party (UKIP) head Nigel Farage countered that the European Union was no longer fit to face the challenges of the modern economy.
Clegg and Farage, who wants to pull Britain out of the EU, will meet again for another debate on April 2.
Farage's party is expected to make large gains in the May 22 elections, while Clegg's is expected to fare badly.
"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," he added.
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Farage said Britain had "sold his birthright" by handing powers to the EU, and vowed to act to reclaim control of lawmaking from Brussels and to cap immigration. But he insisted he wanted to keep close ties with the continent.
But he controversially suggested that the EU had "blood on its hands" over Ukraine, claiming that its desire to create an "empire" had given Ukrainians false hope of being able to counter Russia's influence.
Commentators largely agreed that Farage had dominated the early rounds of the hour-long debate, hosted by London radio station LBC, but that Clegg had hit back later on.
Recent polls show UKIP has moved ahead of the Lib Dems as Britain's third-most-popular political party.
British Prime Minister David Cameron, the Conservative Party leader, wants to renegotiate London's relationship with Brussels and stage an in-or-out referendum on EU membership by the end of 2017 if he remains prime minister after next year's general election.