Ed Miliband said he believed Labour could win an outright majority in May during a heated one-on-one session with Jeremy Paxman, with just over 40 days until the general election.

He followed Prime Minister David Cameron to be grilled by the former Newsnight presenter in front of a live studio audience, during which Paxman suggested Miliband was too weak to lead Britain and voters would prefer his brother, David, was leading the party.

Miliband also faced a question about his battle with his brother over the party leadership when Gordon Brown stood down in 2010 during his Q&A with audience members, admitting the fight had been "bruising" and the siblings were gradually getting over it.

Paxman said there were doubts Miliband could stand up to foreign leaders such as Russian President Vladimir Putin. Asked whether the Labour leader thought he was "tough enough" to be prime minister, Miliband retorted: "Hell yes, I am tough enough."

Both Miliband and Cameron had an 18-minute grilling by Paxman, as well as a Q&A session with audience members. The prime minister was asked repeatedly by the former Newsnight presenter about zero-hours contracts and the 700,000 Britons who currently worked on them, but he responded that his party had got 1.8 million people in work over the past five years.

He also gave a strong defence of the Conservative plan to cut the deficit and the intervention in Libya, which he said was the right thing to do, despite the fact the country is now on the brink of civil war with Islamic State (Isis)-affiliated groups controlling some towns and cities.

"I think it was right to stop Gaddafi when he was going to butcher his own people in Benghazi. If I hadn't ordered those planes into the sky that would have happened. We're still trying even now. It's been a difficult situation," Cameron said.

The Tory leader was dragged into discussions about planned cuts to welfare that he has largely tried to avoid during the last weeks of the Conservative campaign, confirming his party would seek to lower the welfare cap from £26,000 to £23,000. But he said his government "had achieved everything it had set out to do" over the past five years.

Opinions were divided in the wake of the show, whether Cameron or Miliband won the day, but a snap poll by the Guardian put the Tory leader at 54% compared with 46% for Labour's front man. Indeed, while Cameron did not give a lot away during his grilling by Paxman, Miliband repeatedly spoke of mistakes and failures of the Labour party under Brown and Blair.

But at the same time, the Miliband on 26 March was far removed from the Labour leader who got a mauling during PMQs a day earlier, when he was hit by Cameron's bombshell announcement that the Conservatives would not raise VAT during the next government.