The two leaders appeared separately, taking questions from the audience and were then grilled by Jeremy Paxman.
The Labour leader chose to be first up for a grilling in the Battle for Number 10 show, which was broadcast by Sky News and Channel 4, after winning a coin toss.
The leaders did not appear together because Mrs May had declined to take part in a head-to-head debate with other party leaders.
Mrs May defended her social care reforms and was repeatedly asked if she had really changed her mind about Brexit, since she had been on record as supporting the Remain campaign during the Referendum last year.
Theresa May also took questions on the NHS – while Jeremy Corbyn was challenged by a business owner.
He was also asked back-to-back questions on Brexit – one from a Leave voter calling for immigration controls and another from an unhappy Remain supporter.
Answering the first, he refused to set a target for migration numbers, saying Labour would act to prevent the undercutting of wages.
He then told the Remain supporter Labour had to “accept the reality of the referendum”.
Questions Unanswered
Mrs May was asked about the Tories’ planned reforms to the way social care is funded, with a man in the audience describing the changes as a “dementia tax”.
The PM confirmed an overall cap would be put on costs, which had not been included in the Tories’ election manifesto, but did not say where this would be set.
Mrs May promised a consultation document would be published and that she would listen to charities and voters on where the cap should be, adding that the social care system would “collapse” without reform.
Other parties’ reaction
Lib Dem Tim Farron said both leaders had committed a series of “blunders”.
He claimed Mr Corbyn had made an unfunded commitment to lift the welfare cap, and Mrs May would not say how many people would be hit by a “dementia tax”.
The SNP’s Patrick Grady said: “I think we’ve found out why the prime minister has been so reluctant to take part in leaders’ debates tonight.”
Plaid Cymru criticised the lack of mentions of Wales, and the Green Party said Mrs May had “avoided the question” on her “unfair” social care reforms.
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