And although there was no clear victor among the bickering, Ms Rudd's combative performance will have boosted her chances of becoming the next Tory Chancellor and a future leader of the party. "She won't turn up to these debates because her campaign of soundbites is falling apart", she said.
Mr Corbyn insisted he was "doing no deals, no coalitions" and was "fighting to win this election".
Oduba said critics viewed Mr Corbyn as "more of an activist" than a potential prime minister, but Mr Corbyn said: "Is there a difference? By contrast, Theresa May's refusal to take part showed her weakness".
The Labour leader hit back by accusing the government of offering five more years of austerity "to fund tax handouts for the wealthy few".
The Tories are to be represented by Home Secretary Amber Rudd, after Mrs May made clear that she would not take part in a face-to-face showdown with any other party leaders during the campaign.
"Have you seen the levels of poverty that exist because of your government's conscious decisions on benefits?"
Her assessment garnered more than 9,000 retweets.
Challenging Mrs May to join him at the event, Mr Corbyn told a rally: "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". "We have to stop thinking, as you do, that there is a magic money tree".More news: House intelligence committee subpoenas Michael Flynn, Michael Cohen
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"He is not prepared to take action against terrorists".
"That is what happens if you demonise immigrants", he said.
"Because intrusion in my life is not nice but I am there, I'm an elected politician, it kind of goes with the territory, you might say".
"We can't be sure Theresa May is going to achieve her political objective of a landslide majority", he said.
Mr Corbyn was forced to defend his speech last Friday linking United Kingdom foreign policy to terrorism at home, claiming British military intervention in countries such as Libya had left "ungoverned spaces" which the extremists had been able to exploit to mount attacks.
Mr Corbyn responded that Mrs May and other senior Conservatives had voted against anti-terror laws in 2005.
Ms Lucas, in her closing remarks, said Britain was at a crossroads between tolerance and openness or turning inwards towards "isolation and hate".
"Where do you think Theresa May is tonight? Don't give her yours".