Mr Corbyn replied: "It will cost.it will obviously cost a lot to do so, we accept that".
"The point I'm trying to make is that we're making it universal so that we are in a position to make sure that every child gets it and those that can, at the moment get free places will continue to get them, those that have to pay won't and we'll collect the money through taxation, mainly through corporate taxation".
And with campaigning back in full swing following the Manchester attack, May today ramped up her attacks on Corbyn, questioning the Labour leader's ability to step up to the challenges of Brexit and arguing Labour would be prepared to sign up to both Freedom of Movement and the jurisdiction of the European Court of Justice.
But Barnett hit back, saying: "Why on earth are you giving free childcare to people who can afford it?"
Mr Corbyn's most uncomfortable moments during questions from the audience came when it was claimed he had "openly supported the IRA in the past" by attending a commemoration for IRA members killed by the SAS.
Ten days before the snap polls on June 8, the two rivals separately faced wide-ranging questions from members of the public before interrogations by veteran bulldog broadcaster Jeremy Paxman.
Ms Barnett said: "I presume you have the figures?"More news: Frontline Ltd. (FRO) Stock Is At Yearly Low Now
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"No deal is better than a bad deal", the 60-year-old prime minister repeatedly said in the Sky News/Channel 4 "Battle for Number 10" broadcast.
Corbyn insisted that all of Labour's manifesto policies had been fully costed and will be funded mainly through raising taxes for the top 5% earners and corporations.
But Brexit Secretary David Davis said Mrs May "brought it back to the fundamentals" over Britain's European Union exit, while Home Secretary Amber Rudd said Mr Corbyn's answers were "really worrying for security".
Her assessment garnered more than 9,000 retweets.
"Strong and stable leadership is about being open about the hard choices that lie ahead, in order to build that strong government, and strong and stable leadership is about having a plan to take us through those Brexit negotiations and a plan to take Britain beyond those Brexit negotiations and build that stronger, fairer country for all".
With its main goal of Brexit having been achieved, the United Kingdom Independence Party (UKIP) has seen its support dwindle from nearly 13 percent two years ago to five percent in the latest polls.
"In the last week alone more than 65% of bets have been on Labour, however nearly 95% of money is on the Tories, who are still heavy odds-on favourites at 1/14", she said.
Earlier, a separate survey by YouGov found that Labour's lead among voters under 50 is growing after the Tories' revealed unpopular social care policies for pensioners.