The veteran newsman also took the prime minister to task over her u-turns on National Insurance rises and an early election.
The Labour leader was challenged seven times on how much money would be needed to extend the provision of 30 hours of free childcare a week to all two to four-year-olds. But a voter not versed in these details might have accepted Corbyn’s claim that he was juts pushing for a Good Friday-style deal.
Corbyn replied: “All of our manifesto is fully costed”.
“If the Conservative story is how Theresa May is the “brand leader”, the interesting thing is that a lot of Labour supporters really like and believe in the messages that Jeremy Corbyn is bringing across”, he said.
The renewal of Trident was “a conference decision by the Labour Party and as the leader of the party I accept the democracy of our party”, the leader added.
Mrs May was also pressed about the Conservative Party’s social care plans, dubbed the “dementia tax”, with one elderly audience member asking: “Why should we in my generation vote for you?”
As well as questions about security in the wake of Manchester, he was also scrutinsed on past comments about the IRA and the Falklands War.
Mrs May, who was at times heckled by the audience during the televised questioning, was asked by a serving policeman about “devastating” cuts to police numbers during her six-year tenure as interior minister. “It’s actually about what the police are able to do and how they are being deployed on our streets”.
There are several possible reasons for this: Labour’s popular manifesto policies and Theresa May’s controversial social care plans and subsequent U-turn nearly certainly contributed strongly to a shift in public perceptions. “Everybody should have the chance to study education for free”, he says, adding that the amount of debt he’s personally racked up nearly put him off going to uni.
“We need to face up to the fact that there are going to be extra costs and we think this is the best way to handle it and I think the audience responded well to that honesty”.
The Prime Minister said that the funding of the health service is linked to the performance of the economy, but she was committed to increasing funds for the NHS.
Paxman thought he had scored some debating point when she refused to say directly that she would “walk away” from the talks if she couldn’t get what she wanted, but all he had done was allow her to explain, with some force, what she meant by saying “no deal is better than a bad deal”.
“Let’s deal with the Brexit negotiations first”.
For the Conservatives, International Development Secretary Priti Patel said Mr Corbyn’s “chaotic radio interview with Emma Barnett” showed the British people “why he is simply not up to the job of being the prime minister”.
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.