But Mrs May said: "I'm not refusing to take part in debates, because I'm here answering questions from you".
May's once-formidable lead has been eroded though her Conservative Party could still be on course to win a majority of seats in parliament, an opinion poll and an electoral model showed on Friday.
She continued: "I could have stayed on doing that job for another couple of years and not called an election".
"Set free from the shackles of European Union control, we will be a great, global trading nation once again bringing new jobs and new opportunities for ordinary working families here at home", said May, who backed the "Remain" campaign for last year's referendum on European Union membership.
Dr Lelliott said it was only a few weeks ago that some key allies of Labour leader Jeremy Corbyn were saying Labour would be lucky to get 200 seats.
The two leaders were being quizzed consecutively and during May's outing the audience zoned in on her U-turns over the calling of the General Election and on social care.
"And I believe they should have a prime minister with a resolute determination to carry out their will".
"I don't think people have ever truly loved this government in the way the Thatcher or Blair governments had true believers and a big, enthusiastic base of support".
"That's what I think is important in an election campaign - not politicians arguing amongst each other, but actually listening and taking questions from voters".
Listing proposals to pump more resources into education and mental health care, Mr Corbyn said: 'We have to respect the needs of people and challenge all of us to say that if we want to live in a society that genuinely cares for all, we've got to be prepared to deal with issues of inequality and pay for it.
One woman asked why voters should trust her given her "track record" of "broken promises" during her tenure.
Mr Corbyn said Labour was "not looking to do deals with anybody" when asked if he would seek the support of the SNP.
All fairly predictable knock-about stuff but the main question which senior Labour figures would like to linger in the minds of voters is why should we have confidence in Mrs May to go into the negotiations when she does not have confidence in her own ability to enter a leaders' debate? Survation interviewed 1,049 United Kingdom adults online on June 3.
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