The "Battle for Number 10" show broadcast on Sky News and Channel 4 brought the two prime contenders together in the same studio at the same time, but they did not appear together at any point.
She will promise to use Brexit to make the United Kingdom a fairer society and focus more on the concerns of working people who struggle to make ends meet.
"We won't start the negotiations with megaphone diplomacy, threatening Europe with some kind of offshore tax haven on the shores of Europe", he said in a dig at May's efforts to handle Brexit.
The studio audience again applauded loudly when Mr Paxman pointed out that Mrs May and her spokesmen had promised on six occasions since becoming PM that there would not be a general election before 2020. "That's why I thought it was right to call an election".
"We will put an absolute cap on the level of money that people have to spend on care".
He said: "The more they avoid exposing the deficiencies of Theresa May to public scrutiny, the more people are beginning to realise that she's not up to the job".
British prime minister Theresa May faced laughter, jeers and heckling from a studio audience on Monday night as she struggled to answer questions about her record during a TV interview with Jeremy Paxman.
"First and foremost we say that we would guarantee the rights of European Union nationals living in the United Kingdom", she said.
Mrs May said that when she took office she felt the most important thing was to maintain "stability" in order to get on with Brexit, but that she had found that her opponents wanted to "frustrate" the process.
When asked whether he would contemplate a scenario where Britain failed to strike an arrangement with the rest of the bloc, Jeremy Corbyn said: "There's going to be a deal". "In negotiations you have to recognise that you're not in there to get a deal at any price". He insisted Labour wouldn't "soften" United Kingdom foreign policy in the wake of a speech in which he said overseas military interventions had make the country less safe.
The Labour party condemned today (Monday) its candidate in the upcoming British elections, MP Jeremy Corbyn, after he admitted attending a wreath-laying ceremony at the grave of a Palestinian terrorist involved in the 1972 Munich Olympics massacre. May is attempting to drive home the message that she'll provide "strong and stable" leadership while Labour can't be trusted to defend the country. She replied: "I think you have to".
The Tories were hoping to "avoid exposing the deficiencies of Theresa May to public scrutiny" by criticising the Labour leader, said Tom Watson, whose words were significant, given his own relationship with Mr Corbyn is often rancorous. "Sometimes you have to be hard in order to do that".