There were questions about Mrs May’s dementia tax U-turn, the Government’s cruel fitness-to-work tests for disabled people and school funding.
Meanwhile Mr Corbyn was grilled over his views on Trident nuclear missiles and the IRA.
Here we’ve taken a look at the most uncomfortable moments at each of the two leaders during the 90-minute Q&A session at the University of York…
When Theresa May was skewered by a disabled woman over fitness to work tests
An audience member – who is partially sighted, has mental health issues and spent 18 months on an NHS waiting list for counselling – blasted the Prime Minister.
She said: “It’s so important. The NHS is an absolute shambles for mental health at the moment.
I applied for NHS counselling about, I think, at the end of 2015. My first appointment is next Tuesday.
I went into my assessment and I was asked in detail about suicide attempts and I came out crying because I was so upset I was treated by that nurse.
She came out after me. She had forgotten to test my eyesight.
When the Prime Minister was asked why she’s always doing U-turns
The programme began when audience member Abigail asked Theresa May why she’s always doing U-turns.
She said: “You have back-tracked as Prime Minister, you back-tracked when you became leader of the Conservatives and immediately after the EU referendum.
You said you wouldn’t call election and you are here calling an election, refusing to take part in debates, refusing to answer people’s questions, refusing to talk to Jeremy Corbyn and you have back-tracked on your social care policy and your entire manifesto has holes in it and everyone else can see that.
This was met with loud applause and Mrs May replied: I thought we needed a period of stability when I became Prime Minister… but what became clear to me is other parties wanted to frustrate those Brexit negotiations.
When Theresa May’s dementia tax plans were blasted
One audience member asked the PM: What is the point of us working our whole lives and building up a pension if it’s all going to be taken away again to pay for our care should we need it?
She replied to say there would be a consultation to get the policy right – including over the level of the proposed cap on social care costs.
She said: What I want to do in relation to the details on the policy including level of cap is to consult with people and voters, charities and organisations working with older people.
I think that’s a fair way to do it rather than just producing a figure now.
When Corbyn was asked why he has never called the IRA terrorists
Challenged by the audience about why he never called the IRA terrorists, Corbyn found himself in a tricky situation.
The Labour leader said he deplored terrorist acts by all groups in Northern Ireland.
Challenged again by the audience member who said they did kill a lot of people, didn’t they?
Corbyn again refused to deal with the IRA specifically. All deaths are wrong, he said.
The Labour leader added: But you have to bring about a peace process by talking to people you don’t agree with if you only talk to your friends, you don’t get a peace process.
When the audience pleaded for Corbyn to ‘answer the question’ on Trident
There were audible groans of frustration from the audience when Corbyn refused to answer a question about using nuclear weapons in a crisis.
Mr Corbyn said: I think the idea of anyone ever using a nuclear weapon is utterly appalling.
Answer the question, one man pleaded.
The Labour leader has been anti-nuclear for decades and said he would not use nuclear weapons first.
He went on to say he wouldn’t use them in retaliation because millions would die.
When he floundered on the benefits of zero hours contracts for students
A student in the audience asked: Zero hours contracts provide an easy way for students like myself to get casual, flexible work. How will scrapping such contracts affect us?
Corbyn replied that in general zero hours contracts were negative, but didn’t really address students at all.
Zero hours contracts, for many people, mean a liftetime of stress and great difficulty, he said.
He said that he understood “the point about students” and the need for flexibility.
But he said employers should draw up contracts that work around the schedules of their staff members.
It’s not simple for employers but it gives them a wide range of workers who will be loyal.