Nick Clegg reveals live on the radio he owns a onesie, but has never worn it ITN

Nick Clegg made radio history on Thursday morning, taking live questions from listeners of London's LBC radio and subjecting himself to criticism from some callers angry at the role the Liberal Democrats are playing in the coalition.

It was, as presenter Nick Ferrari assured listeners, "a wild and wonderful ride", in which Clegg defended coalition policies – and admitted to listeners that he owns a "big green onesie".

With questions that ran the gamut of Lib Dem frailties – from cuts that affect the poorest in society, to Europe and the hike in university tuition fees – Clegg met difficult and occasionally hostile callers with a barrage of Lib Dem policy examples.

The 30-minue show, entitled Call Clegg, began its first weekly airing at 9am, the first time such a senior UK government figure has agreed to be grilled on a regular basis by listeners.

After a relatively tame opening, where Clegg was praised for the "commendable" move of coming on the show by a caller, he was confronted with a former Lib Dem county councillor who told Clegg he had "torn up" his membership and asked how the deputy prime minster could reconcile the Lib Dem values with "this government's attacks on the poorest".

Clegg responded that the Liberal Democrats had taken "big, collective and brave" decisions, and referred to apprenticeships, free nursery education and the pupil premium as a measure he had "personally pushed through" to help the poorest in society.

Another difficult call came from Lauren, a journalism student at the University of Sheffield, who asked how young people could trust the Lib Dems after tuition fees rises, which the Lib Dems promised to oppose before the election.

Clegg responded that the new system, "a kind of graduate tax", allowed students to avoid paying fees upfront with a higher threshold for repayments. "Whether you or I like it we are living in a country at the moment facing the consequences of one of the biggest independent meltdowns in this country's history," said Clegg.

Pushed by Ferrari he admitted he regretted the policy U-turn. "It is certainly one of my biggest regrets that we made a commitment we weren't in position to deliver," he said.

He defended defence cuts after a call from a military wife and told another caller that giving £8bn in overseas aid was not just morally right, but in Britain's interests.

Responding to a question about recent American comments regarding Britain's membership of the EU, Clegg said: "If you want to lead around the world you've got to be strong in your neck of the woods – I think that's what they are saying," he said, adding that the remarks had not surprised him as the US had always wanted the UK to have a strong presence in Europe. Asked if he had spoken to David Cameron on his pro-Europe stance, he said "of course, I've said it again and again".

The deputy prime minister's decision to appear on the weekly show is widely considered to be an attempt to revive his personal approval ratings, which are the worst of the three main leaders. His party is at 9-14% in the polls, behind Ukip, which appears to have supplanted the Lib Dems as the natural party of general political protest.

Ferrari, pressed Clegg on his and his party's unpopularity. Clegg responded that joining a coalition would make any party unpopular, but added: "Where we can get on a doorstep – or a microphone – and explain to people why we're doing what we're doing … people see why we are making the decisions we are." He admitted the party's 8th place finish in a recent Rotherham byelection was a "woeful result".

The question that provided perhaps the most enduring image from the phone-in came from Harry in Sheffield, who asked the deputy prime minster if he was a "man of the people" and had ever worn a "onesie". Clegg replied: "I was given a big green onesie in Sheffield, which I have not worn, it is still in its wrapping". Asked if he would wear it Clegg did not rule it out, but said it would be in the comfort of his own home.