She rebuffed his repeated attempts to get her to say whether she now thinks leaving the European Union is a good idea, saying only that the British voters have decided and that she is determined to get the best deal possible.
Ms Barnett said: "I presume you have the figures?"
"You have to. In negotiations, you have to recognise that you're not in there to get a deal at any price".
Jeremy Corbyn faced lengthy questioning on foreign policy and security, defending his claim that the killing of Osama bin Laden was a "tragedy" because the al-Qaeda chief should have been put on trial.
Liberal Democrat leader Tim Farron will be in Bermondsey, a seat his party lost in 2015 and will be hoping to regain.
Mr Corbyn's attempt, in the wake of the Manchester terror attack, to draw a link between British involvement in military interventions overseas and terrorism at home led to allegations he was making excuses for extremists.
May was heckled and laughed at by some members of the audience at Monday's TV appearance when discussing her education policy, and when interviewer Jeremy Paxman asked whether the European Union would see her as a "blowhard who collapses at the first sign of gunfire" after she softened her plans on old age care.
Mrs May faced questions on controversial social plans, cuts to the police and health spending in England, and was challenged over whether her boasting about being called a "bloody hard woman" risked returning the Tories to the "nasty party" image which she fought against in the past.
Mr Corbyn has made clear that his own marriage is out of bounds to the media, and third wife Laura Alvarez will not be subjected even to the gentle grilling of The One Show team.
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That's a little bit sad, but that shows different individuals have stepped up at different times and taken up responsibility. Parthiv Patel is one of the few players that have been part of the Indian Premier League setup since its inaugural season.
Challenged over whether he would "soften" the UK's foreign policy, Mr Corbyn said: "It's not about softening our foreign policy".
When asked whether he would contemplate a scenario where Britain failed to strike an arrangement with the rest of the bloc, Corbyn said: "There's going to be a deal".
He could be prime minister in 11 days' time if he closes the single-figure gap which some pollsters have described and tonight the public audience, Faisal Islam and Paxman all focused on Corbyn's qualities as a leader.
He added: "You don't address these problems by ignoring them".
On immigration, he claimed under Labour's plan for "managed migration" it would not go up but would "probably" come down from its current level of around 250,000.
Mr Corbyn defended his description of the Palestinian group Hamas as "friends" and his comment that the killing of Osama bin Laden by U.S. special forces had been a "tragedy". "The amount of debt that I have, personally, it nearly put me off going to uni".
So, in effect, voters will decide whether May or Corbyn gets to sit down with Brussels and hammer out an exit deal that will define the country's trade and diplomatic ties with the EU.
"It is a hypothetical question", he said.