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The Labour and Conservative leader will face questions from the audience in York separately
Mrs May was repeatedly challenged over her decision to call a last minute snap election, after insisting she wouldn't.
One Tory supporter in the audience asked if she regretted and felt "remorse" about the decision because of the shrinking poll gap.
But Mrs May repeated her mantra that "the only poll that matters is the one that takes place on polling day" and insisted she was right to have the "balls" to go to the country.
Theresa May said she had the balls to call an election
She said: "It would have been the easiest thing in the world for me having become Prime Minister after the referendum, when David Cameron resigned, to say 'the next election is not 'til 2020'.
"In this job I do what I believe is the best for Britain. I could have stayed on doing that job for another couple of years and not called an election.
"I had the balls to call an election."
In a swipe at the prospect of Labour running the country, she said: "We have a situation at the moment where if Jeremy Corbyn was to get into Number 10, he'd be being propped up by the Liberal Democrats and the Scottish nationalists.
"You would have Diane Abbott who can't add up sitting around the Cabinet table, John McDonnell who is a Marxist, Nicola Sturgeon who wants to break our country up and TIm Farron who wants to take us back into the EU – the direct opposite of what the British people want."
Mrs May also blasted the bureaucrats in Brussels while reaffirming her insistence not to hold another vote on EU membership.
The prime minister dismissed holding a second referendum, something the Lib Dems have been pushing for, on the terms of the Brexit deal.
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Theresa May vowed to push through Brexit
Mrs May said: “Over the years in the European Union and its European economic community there have been a number of occasions where referendums have been held in countries, there was one in Ireland, I think France is an example as well, where ethic voted against what the EU was suggesting.
“And basically the bureaucrats and the EU politicians turned round to the countries and said you’ve got it wrong, have another vote we want we want you to come up with what we think is the right answer.”
It was important to listen to the will of the people and deliver Brexit, she said, not bow down to pressure and hold a second vote, something which would have delighted Brussels who voiced their displeasure with the No vote.
The two leaders faced questions on the BBC show from 8.30pm on Friday night, but didn't go head-to-head.
The Labour and Conservative leaders faced questions from the audience in York separately, in one of two election programs to be aired in the run-up to the crucial vote on June 8.
The Q&A sessions comes just days after Mrs May refused to take part in a seven-way leaders debate on Wednesday, sending Home Secretary Amber Rudd in her place.
She was widely criticised for her no-show, something rival Jeremy Corbyn attempted to capitalise on.
The 90-minute program did not see the pair debate, which Theresa May has actively tried to avoid.
The format is similar to when the pair faced questions from Jeremy Paxman on May v Corbyn Live: the Battle for No 10 earlier this week.
They were quizzed on a range of topics including nuclear disarmament, Brexit, schools and social care policy.
The second Question Time debate takes place on Sunday night between Liberal Democrat leader Tim Farron and Scottish National Party’s Nicola Sturgeon.
Here Express.co.uk delivered live updates on the crunch Question Time debate. Follow our coverage below.
Security has been ramped up at the University of York
9.59pm update: Asked why university fess are a priory to scrap ahead of other issues, costing, £11 billion he said it was important to give everyone “real access” to higher education.
He said his generation should not ‘pull up the ladder’.
9.57pm update: Mr Corbyn said it was crucial to maintain an economic relationship with the EU.
9.56pm update: He said the corporation tax level would be lower than most western industrialised countries.
9.54pm update: Mr Corbyn has been labelled a ‘socialist with a red book’.
9.53pm update: “I have not supported any of these organisations”, in response to a question about Hamas.
He said you have to talk to people you do not agree with to bring about a peace process.
9.51pm update: Grilled over not labelling the IRA as terrorists, he said he deplored all forms of terror.
He said: ’I don’t approve of any terror or terorirsm of any sort’
Refusing to agree they killed a lot of people, he replied: “All deaths are wrong all killing is wrong.”
9.50pm update: It would be “not simple to manage” for employers.
9.49pm update: Speaking about zero-hours contract, he said for most people it was a “source of stress”.
He said he understood the point of view of students who enjoyed the flexibility.
9.47pm update: He is being grilled over his living wage policy to £10 by an audience member.
Mr Corbyn admitted that small companies may have problems if it was implemented.
But he said he thought it would be an economic boost.
The pair did not know the questions being asked to the
9.45pm update: He admits immigration was a big factor in the Leave vote last June.
Mr Corbyn said he would restore the Migration Impact Fund.
9.44pm update: He said there will “probably” be some reduction in European migration.
“We will end overseas only recruitment”.
9.43pm update: Asked on his immigration policy, he did not confirm if he was in favour of reducing immigration.
9.40pm update: He was pressed over whether, as PM, he would press the button, Mr Dimbleby accused him of dodging the question.
Mr Corbyn again championed disarmament, but was pushed on the issue by the host leading to applause from the audience.
“We would not use it as first use, if we used it millions would die.
“I’ll decide on the circumstances at the time.”
9.39pm update: “We’ve only got one planet” he said as he urged people not to destroy it.
9.37pm update: Despite Labour party committing to keep Trident, he said using it would represent a “failure” and championed global nuclear disarmament.
When asked if he would push the button, he saud the weapon is there but “no first use of the weapon”.
9.35pm update: He has condemned the use of nuclear weapons anywhere in the world.
9.34pm update: Blind application for jobs has been mooted as one possible policy to deal with racism and discrimination.
9.31pm upate: Mr Corbyn is being grilled over his 'failure to take Ken Livingstone to task over anti-Semitic remarks’.
“We have a process which is independent of me.”
He said he deplores racism in any form.
The TV election debate – in pictures Wed, May 31, 2017
The televised debate saw Jeremy Corbyn, Amber Rudd, Paul Nuttall, Caroline Lucas, Angus Robertson, Tim Farron and Leanne Wood go toe-to-toe
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The politicians taking part in the debate
9.30pm update: He said the manifesto is a well-thought out document, and it was time to rebalance society.
“The very richest in our society have got richer.”
9.28pm update: An audience member has asked if the Labour manifesto is a “letter to santa Claus”.
Mr Corbyn says they have been “brave” to put it out there.
“It’s time for us to invest in our future.”
9.27pm update: The Labour leader said the government would get £48 billion more.
9.24pm update: Mr Corbyn is defending hid tax hike proposals, saying it will be lower than the G7 average.
He said he thought it was “worth it” for a better society.
9.23pm update: Mr Corbyn said they were fighting this election to win, and was not seeking to forma coalition with any other party.
Brandishing his manifesto he said “no deals”.
He was determined to pursue protection of the environment, saying he found Mr Trump’s actions “deplorable” and would sign any letter condemning his action.
Jeremy Corbyn is being grilled during the debate
9.20pm update: Leaving the EU means an “independent and separate relationship with the EU.
His aim was to have a tariff-free trading relationship with the EU.
9.19pm update: His ‘no deal is a bad deal’ policy has been critiqued.
“We’re not approaching these negotiators by threatening Europe.”
“A sensible relationship with them is important.”
9.18pm update: “I hope we will have aLabour government which will be investing in a growing economy.”
9.17pm update: He begins by blasting his rival for to taking part in a debate.
Mr Corbyn says he will immediately legislate to ensure the rights of EU nationals living in the UK and praised Kier Starmer.
The first half of the programme has ended, with Labour leader Jeremy Corbyn now facing questions.
9.15pm update: After facing questions on education and the NS, she is now being grilled over her stance on Donald Trump pulling out of the Paris Agreement.
When asked what she said, she said he has taken the decision backs ehe thinks its in the best interest for America.
“I’ve told him my views.”
9.13pm update: A quality education was not just about pumping money into schools, but the “innovation and creativity” in education.
8.58pm update: “In the five years to 2020 we will be spending half a trillion on the NHS.”
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8.57pm update: Mrs May is setting out why they are not following the Dilnot recommendations.
8.55pm update: She said they were going to “consult with people, consult with voters, consult with organisations” before imposing any figures.
8.53pm update: "We'll consult on the cap."
"If we do nothing our social care will collapse."
Speaking on her social care u-turn, she was defending he figures against Mr Dimbleby, pointing out there is a “cap and a floor”, which she was challenged over as the host said it was not in their manifesto.
8.51pm update: Defending her manifesto, the lack of costing and the u-turns, she said as a politician on the whole: “We are asking people to trust us.”
8.50pm update: Responding to calls she should have the “confidence” to call a second vote she referenced previous referendums in various EU countries.
She said: “Let’s listen to the people and actually deliver on it.”
Sshe said the only poll that mattered is the one on the day
8.48pm update: An audience member pointed out despite her comments about Ms Abbott chancellor of the exchequer Phillip Hammond made a £20 billion mistake.
8.47pm update: “They want to start off talking about the bill.”
A good deal in trade terms would benefit not just the UK but the remaining 27 members, she said.
8.46 update: Mrs May could not give a figure for what a “good deal” would look like for the UK.
8.44pm update: Defending her record as a Remain voter, she said: “I also said the sky will not fall in if we leave the EU”.
8.43pm update: She was grilled over what she thought a ‘bad deal’ for Brexit is, and is now explaining how she can represent the whole of the UK when only 52 per cent voted to leave.
Mr May said she "believes in the British people" and called Brexit an "opportunity".
8.41pm update: She is once again having to defend her refusal to debate with the other leaders, calling it “more useful” to be out and about listening to voters.
The PM called it “seven politician arguing among themselves”.
8.40pm update: A passionate audience member as told her calling an election will “backfire”.
Mr May has said she could have easily stayed in the job, but called the election for the good of the county.
8.38pm update: When asked how she felt now the polls showed her lead over Labour thinning considerably, she said the only poll that mattered is the one on the day.
Mr Dimbleby now asks if she is “surprised” her lead has dropped from 20 points to five.
8.37pm update: “We got the article 50 legislation through parliament . . . whoever comes in as a prime minister as a government has to be ready to get the ball rolling.”
She said it was “clear” other parties wanted to frustrate the Brexit process. She took another swipe ta Ms Abbott, saying she "can’t add up."
8.35pm update: “I’ve called an election because of Brexit.”
8.34pm update: The audience member is now taking Mrs May to task, detailing all her u-turns and policy swerves. She also attempts to defend why she did not take part in the leaders' debate.
8.33pm update: When quizzed over he backtracking and u-turns as her time as Home Secretary and Prime Minister, Mrs May is reeling off a list of her achievements. She also took a swipe at shadow Home Secretary Diane Abbott.
8.30pm update: The BBC show is underway with Mr Dimbleby opening up the programme. He says one third of the audience are backing Conservatives, Labour or are undecided.
He confirmed they do not know the questions being asked to them, and Mrs May is up first.
8.20pm update: Theresa May and Jeremy Corbyn have been seen entering the University of York ready for their sit-down with David Dimbleby.
Security has been ramped up at the University of York, with an increased police presence stationed around the building.