Theresa May has joked she needed a "stiff drink" after her calamitous Tory conference speech but insisted voters have backed her on the doorstep.
The Prime Minister said husband Philip had been a "bit worried" about her safety after a prankster confronted her while she was on stage, but insisted she had never felt unsafe.
The speech sparked a botched attempt at a coup that quickly fizzled out followed by calls for a Cabinet reshuffle.
Mrs May refused to divulge whether she was planning to move round her top team, telling LBC: "Everybody can speculate away to their heart's content."
Asked if she was frustrated by Foreign Secretary Boris Johnson, she replied: "Boris is Foreign Secretary" and insisted he backed her plans for Brexit.
During the LBC phone-in, caller Andy, from Newcastle, a Conservative Party member, told the PM the "longer you cling to power" the greater the certainty of Jeremy Corbyn taking power.
Mrs May reaffirmed her plans to lead the party into the next election, insisting she is "not a quitter".
Being struck down by a debilitating cough during her keynote conference speech meant International Trade Secretary Liam Fox's former life as a GP put him top of the list of potential companions if she was ever stranded on a desert island.
She told LBC: "The name that first went through my mind, maybe it's just because I have had a bad cough, is perhaps Dr Liam Fox would be very practical."
Mrs May slapped down former party chairman Grant Shapps, who last week went public as the ringleader of an attempted coup against her leadership.
Asked whether she was angry with Mr Shapps's actions, the PM said: "I take a very simple view in politics and I have taken it ever since I came into politics.
"I think when you are in Parliament and in a party, you should have any disagreements, any arguments, any discussions about policy and about the way the party is going, in private.
"There will be differences of opinion. You sort those out and then you ensure that you are working together and people support the leadership. I think that's what people should do."
She added: "I have parliamentary colleagues who have a variety of views in this world.
"What is important is that you get on with the job in Government and that is what we are doing."
Comic Lee Nelson, real name Simon Brodkin, handed the Prime Minister a fake P45 unemployment notice during her conference speech and joked Mr Johnson had asked him to perform the stunt.
Mrs May said there had been a moment where she thought "has something gone wrong, am I supposed to be stopping?" but then realised it was not someone official.
"I thought I'd just carry on," she said.
Mrs May said she did not think "at any time" about stopping the speech when she was then hit by a persistent cough that left her struggling for most of the hour-long event.
The PM said her husband was "obviously feeling for me" as she carried on.
"I think he had been a bit worried about the individual who approached me, probably more so than I had been on my position up there on the podium.
"As everybody now knows, he gave me a really big hug because he just wanted to say well done for getting through it."
She added: "I think I probably needed a stiff drink afterwards."
The first caller, Helen from Horsham, asked the PM "why on earth didn't you have some cough remedies with you?", saying she "didn't seem very prepared" after struggling for days.
Mrs May said: "I had had a cough sweet before I went on and had had some cough medicine earlier, so I suppose I just thought it would probably be OK."
The PM said the impression she had been given by voters out on the doorstep was "good on you for carrying on".
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