Ukip member Abigail Eatock won loud applause as she told the PM: "You said you wouldn't call an election and you did".
May had said she was too busy "thinking about Brexit negotiations" and "meeting voters" to take part in the debate.
Mr Corbyn was challenged about his approach to Brexit and said the United Kingdom would not "necessarily" be poorer as a result of leaving the European Union.
Mrs May faced hostile questions over her plans for elderly care, dubbed the dementia tax, and her failure to put a figure on the cap on social care costs she promised after consternation in Conservative ranks over the policy as it was set out in the manifesto. It would have been easy for me as prime minister to stay on and keep a hand on the job.
"That's what I think is important in an election campaign - not politicians arguing amongst each other, but actually listening and taking questions from voters". It is subtitled: "On June 9th, this man could be Prime Minister".
The leaders of the two main parties face audience questions separately in a special edition of the BBC show, presented by David Dimbleby.
"We have a situation where if Jeremy Corbyn was to get into number 10, he'd be being propped up by the Liberal Democrats and the Scottish Nationalists", she said.
Perhaps the highlight of Corbyn's Q&A session came when his opposition to the use of nuclear weapons was challenged by audience.
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He apologised to his family, friends and fans, adding he would "do everything" in his power "to ensure this never happens again". He was arrested about 3 a.m. and released a few hours later on his own recognizance with no bond, according to records.
"There has to be no first use, there has to be a process of engagement to bring about, ultimately, global nuclear disarmament.
We have to be prepared to go in there, recognising that we're not willing to accept a bad deal".
"I'm afraid there is a lesson here about Jeremy Corbyn's psychology and his politics and his naivety, with which he approaches not just the logic of the nuclear deterrent but also the Brexit negotiations".
Mr Corbyn was pressed by the audience over whether he would pursue a coalition deal with the SNP in the event of a hung parliament and the Labour leader insisted there would be "no deals".
The Labour leader responded: 'I urge you to read it.
ICM boss Martin Boon said: "A lot of polls showing a much narrower gap depend on whether you think young people and 2015 non-voters will actually turn out to vote on this occasion".
She added she would continue to work for a Labour party that "once again can deserve your confidence".