"I invite her to go to Cambridge and debate her policies, debate their record, debate their plans, debate their proposals and let the public make up their mind", he said.
SNP Westminster leader Mr Robertson said his party would hold the Tories to account on Brexit, welfare and protecting public services, and vowed to offer "a strong voice for Scotland" in Westminster.
Mr Corbyn said analysis from the independent Institute for Fiscal Studies showed that the Conservative manifesto for the June 8 General Election showed they were offering no new money for the NHS and a real-terms cut in per-pupil funding for schools.
Mr Corbyn, a lifelong opponent of nuclear weapons who has made clear that he would never authorise their use, nevertheless indicated he would issue the customary final instructions to the commanders of the Trident submarine fleet if he became prime minister.
She delivered a pointed jibe against Mr Corbyn by evoking the famous plea of Aneurin Bevan, one of Labour's most revered figures, not to send a Foreign Secretary "naked into the conference chamber".
She argued: "There will be no time to waste, no way of stalling, no way of asking Europe to hang on while we figure out what to do".
May called a snap parliamentary election for June 8 - three years early - arguing that a bigger majority for her Conservatives will strengthen Britain's hand in Brexit negotiations with the European Union.
Mr Corbyn replied: "It will cost ... it will obviously cost a lot to do so, we accept that".
Darren said: "When right-handed people are constructing or coming up with an answer they either have no confidence in or have to answer quickly, their eyes show how they are thinking".
Questioned at a rally in Bath, western England, May said that "debates where the politicians are squabbling among themselves doesn't do anything for the process of electioneering".
"Every single pollster, using whatever method, has found a rise in Labour support and something of a decline in Conservative support", said polling expert John Curtice.
Corbyn performed well on The One Show and looked calm and jovial, just as he did on the Sky News/Channel Four special the previous evening.
Oduba said critics viewed Mr Corbyn as "more of an activist" than a potential prime minister, but Mr Corbyn said: "Is there a difference?"
She was pressed by Mr Paxman over her climbdowns on a proposed Budget hike in national insurance and her social care changes just days after they were unveiled in the Tories' election manifesto - and what it would mean for the Brexit negotiations.
Another said: "Shocked to read that Amber Rudd's father died 48hr ago.even more fair play to her for tonight".
Leaders unite to condemn Theresa May's absence — BBC debate
Corbyn added that the future of the NHS is at stake with patients suffering longer waiting times and hospitals at risk of closure. The PM said she wanted to speak directly to voters and answer their questions rather than "squabbling" with other party leaders.