Jeremy Corbyn has hit out at Theresa May for refusing to debate with him on television, saying it was a "shame" that she had decided not to take part in a head-to-head showdown.
The Labour leader followed the Prime Minister onto a BBC Question Time special, but the two did not face each other in a debate.
Mr Corbyn was challenged about his approach to Brexit and said the UK would not "necessarily" be poorer as a result of leaving the European Union.
The Labour leader said: "I'm very sorry this is not a debate, this is a series of questions. I think it's a shame the Prime Minister hasn't taken part in a debate."
On Brexit, Mr Corbyn defended his team's ability to handle the negotiations, with immediate legislation to protect the rights of EU nationals in the UK and work to "guarantee trade access to the European markets and protection for the conditions we have achieved through EU membership".
He said the "great team of very experienced people" included Sir Keir Starmer, one of the "leading lawyers" in the country.
"I think I can trust Keir Starmer with negotiations more than some other people who are undertaking those negotiations," he said.
Challenged about shadow international trade secretary Barry Gardiner's assertion that the UK would "absolutely be poorer" after Brexit, Mr Corbyn said: "I don't think we necessarily would be poorer.
"I hope that we would retain the trade access and I hope also that we will have a Labour government that will be investing in a growing economy in this country and challenging the terrible levels of inequality that exist in this country at the same time."
Leaving the EU would mean "there is no longer a legislative authority over UK law within the EU or parliamentary consent for it".
There would be an "independent and separate relationship with the EU" after Brexit, he said.
Mr Corbyn hit out at US President Donald Trump over his decision to pull out of the Paris climate change deal - and Mrs May's decision not to sign a letter with other EU leaders condemning the move.
"I utterly deplore Donald Trump's decision," he said. "I would sign a letter with any other leader that would deplore that, straightaway."
The Labour leader insisted he would not strike a deal with SNP leader Nicola Sturgeon and was working for a majority Labour government.
"We are fighting this election to win and we are mounting a fantastic campaign in order to get that message across of how different our society and our politics could be," he said.
"We are contesting all the constituencies. We are not looking to do deals with anybody, we are not forming a coalition government. I want to form a Labour government with a majority to carry out this amazing programme which can give so much hope and opportunity to so many people."
Mr Corbyn was challenged by small businessman Steve Rudd, who said he did not know if he would be able to expand his company and create jobs with the prospect of rises in personal tax and corporation tax if Labour wins power.
"My choice and the choice for my clients is a Conservative government or a Labour government and ... there is a 9% difference between what the Conservatives are proposing for corporation tax on larger businesses and what Labour is proposing," said accountant Mr Rudd.
Mr Corbyn said that under his plans, some small businesses would face no rise in corporation tax rates.
But he defended Labour's plans to ask for a total of £48 billion in additional taxes, to be paid by big business and the top 5% of earners.
"We are asking the very biggest corporations to pay a bit more, but I tell you what - I think it's worth it," said the Labour leader.
"It's worth it so that any young person can go to university and not leave with debt. It's worth it to make sure school headteachers don't have to collect at the school gate in order to pay the teachers' salaries.
"I think it's worth it for a better society in which everyone can achieve something."
And addressing Mr Rudd directly, Mr Corbyn said: "All of your clients, I'm sure, require workers, they require skilled workers, at various times.
"If we as a society don't look at the problems throughout our school and education system and invest in it properly, where are the skilled workers going to come from tomorrow?"
He added: "It's a question of whether the community gets together to support everybody or we just let the rich get richer and the rest suffer."
Asked how he would react if Britain was under imminent threat from nuclear weapons, Mr Corbyn said: "I would do everything I can to ensure that any threat is actually dealt with earlier on by negotiations and by talks, so that we do adhere to our obligations under the nuclear non-proliferation treaty.
"I think the idea of anyone ever using a nuclear weapon anywhere in the world is utterly appalling and terrible.
"It would result in the destruction of the lives and communities and environment for millions of people. And so I would be actively engaged to ensure that danger did not come about."
Audience member Jack Rouse was loudly applauded as he asked Mr Corbyn: "Is Labour's manifesto a realistic wish list or is it just a letter to Santa Claus?"
The Labour leader responded: "I urge you to read it. I think it is a serious and realistic document that addresses the issues that many people in this country face and we've been brave enough to put it out there with all the policies that are in it."
Listing manifesto proposals to pump more resources into education and mental health care, Mr Corbyn said: "We have to respect the needs of people and challenge all of us to say that if we want to live in a society that genuinely cares for all, we've got to be prepared to deal with issues of inequality and pay for it. And I'm prepared to do that."
But Mr Rouse responded: "It's a question of funding it. I'm thinking that last time Labour was in government they left a note at the Chancellor's office saying 'We've no money left'."
Mr Corbyn said that seven years of austerity had left public sector workers under a pay cap, hit public services, caused a housing crisis, while the very richest had got richer and received tax giveaways from the Government.
"It's time to rebalance it," he said. "Our manifesto is a serious, well thought-out document, that I believe is getting a lot of support and people are getting very excited at the idea of how we can do things differently."
Mr Corbyn was heckled as he refused to say whether he would launch a retaliatory nuclear strike.
"I would view the idea of having to use a nuclear weapon as something that was resulting in a failure in the whole world's diplomatic system," he said.
"There has to be no first use, there has to be a process of engagement to bring about, ultimately, global nuclear disarmament. It's not going to happen quickly, it's not going to happen easily, but we have to have that wish."
He added: "People tell me the most effective use of it is not to use it because it's there."
As some sections of the audience shouted, Mr Corbyn said: "If we did use it, millions are going to die. You have to think these things through. I will decide on the circumstances at the time."
One audience member asked if he would "allow North Korea or some idiot in Iran to bomb us and then say 'we'd better start talking'".
Mr Corbyn said: "Of course not, that is why I made the point ... about the need for president Obama's agreement with Iran to be upheld, it's quite important actually, and also to promote disarmament in Korea."
"That is difficult, I appreciate," he added.
Asked if he wanted to reduce immigration, Mr Corbyn said there would be "managed migration" from within the EU after Brexit, as there is currently from outside.
"What I think will happen is there will probably be some reduction in European migration because we will also prevent there being recruitment of groups of low-paid workers from central Europe to come here to undermine existing conditions that are often not very good themselves and damage the life chances of people in this country, and be not actually very good for those that have been brought in," he said.
Mr Corbyn was challenged by an audience member over why he had "never regarded the IRA as terrorists".
Another claimed Mr Corbyn was talking to terrorists while they were "killing our people, our women and children".
The Labour leader said: "I have deplored all acts of terrorism by anybody in Northern Ireland or anywhere else. I think the Good Friday Agreement was a huge achievement that was brought about when both communities recognised their shared but different past and brought about the idea of a power-sharing government in Northern Ireland.
"I think that was an enormous achievement."
He added: "I don't approve of any terrorism of any sort, any terrorist act of any sort. It only divides communities and kills people."
His questioner came back at him: "They did kill a lot of people, didn't they."
Mr Corbyn said: "All deaths are wrong, all killing is wrong."
Another audience member asked Mr Corbyn: "You said you didn't support the IRA, you've also supported Hamas and other terrorist organisations. How do you expect the British people to vote for you to go into Number 10 when you have sat down and supported them?"
Mr Corbyn said: "I have not supported any of those organisations. What I have said is ... if you are to bring about a peace process anywhere, be it the Middle East, be it in Ireland, be it in a different situation in Colombia or anywhere else, there has to be a coming together."
The audience member shot back: "You were talking to them when they were killing our people, our women and children. You were talking to them."
The Labour leader said: "I was talking to representatives of the republican movement, yes. Actually, so was the government at the same time."
Asked if Labour would drive companies out of the country with higher taxes, Mr Corbyn said: "The corporation tax level that I am proposing would actually be less than there is anywhere in the major industrial countries of western Europe anyway."
Challenged on why a Labour government would carry out a strategic defence review, Mr Corbyn said that every in-coming administration undertook one.
"There are serious issues about the shortage of ships in the navy. There are serious issues about supplies of frigates. There's a crucial issue of cyber security. And there is a crucial issue about terrorist attacks."
Mr Corbyn defended plans to scrap university tuition fees.
"It would not be unusual in many other parts of the world to do this. I don't think it's up to me and my generation to pull up the ladder on the generations that are coming behind."
When told that the programme was ending, the Labour leader said: "But I have got so much more to say."
The Labour leader faced claims his plan for a £10 minimum wage by 2020 would hurt businesses, while a ban on zero-hours contracts would reduce flexibility for workers in the so-called "gig economy".
Mr Corbyn said there would be support for small firms to cope with the increase in the wages that employees would be entitled to.
"There are many big companies that could well afford to pay it and shouldn't be just paying the minimum wage," he said.
There were small companies that "would have problems, we fully recognise that" and therefore a Labour government would "work with them, either to give them tax relief or support in order to make sure the real living wage was paid but they didn't close down as a result".
Asked by student Edward Robbins about the zero-hours contracts that offer "casual, flexible work", Mr Corbyn said: "I'm not going to stop you working, it's OK."
But he said firms should offer security to workers: "The agreement should be that you come to a discussion with the employer 'I can work for three hours on a Monday, six hours on a Thursday, two hours on a weekend', something like that, and 'that's my work pattern'.
"It's not simple to manage for any employer, I fully understand that, but it does give security to the individual it also gives the employer a wide range of workers that will be working and will be loyal to that employer."
Asked it he was saying he would "never ever, under any circumstances press the red button" to launch a nuclear strike, Mr Corbyn said: "I think we have discussed this at some length about the aspirations we all have. I do not want to be responsible for the destruction of millions of people, neither do you.
"Therefore we have to work for a world where they are not available and not used."