Look how he's grown: Nigel Farage is a big boy now. If the Ukip leader had one aim in his bust-up with Nick Clegg, it was to sit at the grown-ups' table. No longer simply the party of "fruitcakes" and "closet racists"; or just an insurgent anti-establishment party, a glorified "none of the above" box, there to give the political elite a bloody nose. Farage was standing as an equal with Britain's deputy prime minister, having been granted his greatest national platform yet – a live debate broadcast on Sky News. Despite Farage ending the debate the most visibly sweaty of the two, one of Britain's most senior politicians had failed to duff him up. The implicit message is that Ukip is now a permanent fixture of British politics. Not bad for a party that has no MPs and which has control of not one borough nor city council.

But Farage is always compelled to tread carefully because he leads such an unwieldy coalition. Ukip's leaders are economic libertarians: they advocate a flat tax that would put call centre workers in the same tax bracket as millionaires, and support sacking 2 million public sector workers and scrapping workplace rights such as redundancy pay and overtime. They are most passionate about withdrawing from the EU. But the EU doesn't make the top three concerns of Ukip voters; they are most angry about immigration, and their economic views – on issues such as public ownership, workers' rights and hiking the minimum wage – are firmly on the left. Farage can only flourish by linking the EU to concerns about immigration, and sticking to his folksy brand of "little guy v the elite" populism.

Clegg had a different prize in his sights. "You were the future once," Farage could have told him: easy to forget that the pre-election Lib Dems were a kind of Ukip of their day, the chief beneficiaries of disillusionment with Westminster's two main parties.

Here was Clegg's big chance to prove Lib Demmery was not just doe-eyed Toryism, to burnish his progressive credentials as the man driving back Ukip's xenophobic, nationalist tide. After all, Labour has enjoyed a (currently diminished) lead for so long because it swept up progressive voters who opted for the Lib Dems, only to watch in horror as Clegg exchanged vows with the Tory leader in the rose garden. Clegg is now on a mission to win some of them back.

Farage's pitch was simple. If we were holding a referendum on joining the crumbling EU now, would you vote for allowing foreigners to impose laws on us and give hundreds of millions of people the right to move here? The first question from the audience played to his strengths, and the weakness of both Labour and the Lib Dems: why won't politicians trust the British people by giving them a referendum? Both the Tories and Ukip will take this tack in the run-up to May 2015. They know the EU is not a salient issue for most voters, but linking the referendum to a broader case of trusting the British people could resonate. And with an eye on his complex support base, Farage dabbled with the sort of rhetoric that might be expected from the populist left: "All your gang – all the big corporates," he accused Clegg, had wanted Britain to join the disastrous euro.

Photograph: guardian.co.uk

Clegg responded by wrapping himself in the union jack: he supported EU membership "for the sake of our jobs, for the sake of our clout in the world, for the sake of Britain". He made audacious raids on the tough-on-law-and-order voters that Ukip craves: in the past two years, he said, 149 murderers and 120 paedophiles had been extradited to Britain because of EU membership. Attempts to make the British people embrace the EU with their hearts are long dead; this was an appeal to the head.

If this was a battle to be won or lost on facts, then Clegg won. Two million Brits lived in the EU, he pointed out – did Farage want to repatriate them? Ukip had suggested that 29 million Bulgarians and Romanians would come to Britain, which was greater than their combined populations. To be fair, Farage had a good come-back here: "I am not claiming 29 million have the right to come to Britain," he retorted. "I am saying 485 million people have the total, unconditional right to come to this country."

But the truth is this is not a debate going to be won simply with facts and statistics, and the post-debate snap YouGov poll had 57% naming Farage the victor, against 36% for Clegg. This cannot be put down entirely to Clegg's more unpopular baggage: a recent poll suggested that Ukip was the most disliked mainstream political party in Britain, followed by the Lib Dems. Clegg had been cooler, more refined; Farage was more of a rottweiler, with a few "bloke in the pub" lines thrown in, such as a joke that one bonus from Europe was that "the food is getting better here, and that's great". Despite being, like Clegg, another public school-educated politician, he has two assets: being seen as the outsider, a defiant "up yours" to the establishment, but now with the added credibility of being the leader of what is seen as a mainstream political party.

Of course, this was a debate between two neoliberals, one socially liberal, the other nationalist. The real cures to the anxieties driving the anti-immigrant backlash – falling wages, a housing crisis and insecure jobs – were not debated. Increasing the minimum wage, letting councils build housing on a grand scale, and an industrial strategy would, after all, violate their shared free market dogma. Neither was the case made for a democratised, social Europe run in the interests of working people. But Farage must surely have left the debate satisfied. His party is setting the terms of political debate: the Ukip-isation of politics continues. It will surely only gather pace in the run-up to next May.