The Foreign Secretary looked visibly worried and could be heard saying “oh my god”, as she walked off the stage.
The programme immediately went off-air, with a message appearing on the screen, saying: “We are sorry for the disruption to this programme.
“We are working hard to fix the issue and will return to normal programming soon.”
The broadcaster said in a statement: “Kate McCann fainted on air tonight and although she is fine, the medical advice was that we shouldn’t continue with the debate.
“We apologise to our viewers and listeners.”
After the incident Mr Sunak tweeted to wish the journalist a speedy recovery.
He said: “Good news that you’re already recovering @KateEMcCann.
“It was a great debate and I look forward to getting grilled by you again shortly.”
With the debate ending early, the two leadership hopefuls were then seen chatting to the studio audience and answering questions with the cameras off.
Before it was halted, the two rivals had made a concerted effort to be kinder to each other after a brutal confrontation in the debate one night earlier.
Ms Truss praised the former Chancellor before asking what he would do on day one of becoming Prime Minister to “relieve the money that people are struggling to pay out of their household budgets”.
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Ms Truss told the debate that she would reduce the green levy on energy bills, saying: “The major debate between Rishi and I is about the economy, what I am promising is to deliver tax cuts straight away and to relieve the burden on Sun readers’ pockets and bills.”
Mr Sunak responded he was “going to ask Liz how she was spending her birthday”, saying “Happy Birthday, Liz.”
Answering her question, he said: “On this on this central question, you know what I’ve done over the past couple of years to help the country get through some really difficult times, whether it was creating the furlough scheme that hopefully protected many people’s jobs who are watching and listening tonight.”
He added that one of the last “things I did as chancellor was to make sure that we put support in place over the autumn and winter to help everyone with their energy bills, because I knew they were going to go up, a lot, and everyone’s going to receive help, and the most vulnerable in our society are going to get around £1,200 pounds, so that’s a enormous help with the bills.
“But I’ve always said that I’ll do more as the situation demands it and if it looks as it does look likely now that energy bills are even higher than we thought then of course, I as Prime Minister would come back and do more to help people through because that’s what I’ve done for the last couple of years.”
The debate also saw Mr Sunak insist he was “brave” to introduce a £12 billion tax increase to pay for health social care.
He said: “I made sure we got the NHS the funding it needed to help work through the backlogs, get everyone the care they needed and do that as quickly as possible.
“It wasn’t an easy thing for me to do, I got a lot of criticism for it, but I believe it was the right thing to do as I don’t think we can have an NHS which is ultimately the country’s number one public service priority that is underfunded and not able to deliver the care it needs.
“And that’s why I think you can be reassured the NHS is safe in my hands because I’ve taken what was a brave decision to get it the support it needed.”
Ms Truss said: “I am committed to the extra money that was announced for the NHS. It is needed to deal with the backlog and I would fund that money out of general taxation.
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“Under my plans, we will still be able to start paying the debt down within three years, so it is affordable, and the fact is whatever Rishi says now, we didn’t need to raise national insurance in order to pay, we did have that money available in the budget, it was a choice to break our manifesto commitment and raise national insurance.
“I think it was the wrong choice to make, I spoke out against it at the time in Cabinet, I still remain opposed to it and I’d reverse that rise.”
It came as Boris Johnson compared Volodymyr Zelensky’s leadership of Ukraine to the war-time exploits of Sir Winston Churchill.
The Prime Minister said he believed “Churchill would have cheered and probably have wept too” when the Ukrainian president insisted he needed “ammunition, not a ride” out of Kyiv when the Russian invasion was renewed in February.
He added he could imagine Sir Winston’s “spirit walking with you” and “jabbing the way ahead with his walking stick” throughout every ordeal.
Mr Johnson’s comments came during a ceremony in 10 Downing Street in which he presented Mr Zelensky, who appeared via video link, with the Sir Winston Churchill Leadership Award.
Members of the Churchill family and the International Churchill Society attended the ceremony.
Mr Zelensky said: “This is my extreme honour to receive this award for leadership.
“Ukraine was not left alone after February 24, we had those who were helping us, who remembered in the darkest times what is honour, and who have not thought of quitting the struggle – I’m talking about you Boris.
“This award is yours as well and this is the manifestation of our joint leadership of Ukrainians, Britons and all those who will not give their freedom away to any tyrants.”