Video report by ITV News Reporter Ivor Bennett
The Conservative former prime minister, 52, admitted that he thinks about the consequences of the vote to leave the European Union "every single day" and worries "desperately" about what will happen next.
In an interview with The Times ahead of the publication of his memoir next week, Mr Cameron said he thought another referendum could not be ruled out "because we’re stuck".
"I’m not saying one will happen or should happen. I’m just saying that you can’t rule things out right now because you’ve got to find some way of unblocking the blockage," he said.
In his long-awaited memoir, Mr Cameron reportedly refers to his former Cabinet colleague Mr Gove as “mendacious” and said he and Mr Johnson behaved “appallingly” in the referendum campaign.
He told the paper: “I say in the book: Boris had never argued for leaving the EU, right?
"Michael was a very strong Eurosceptic, but someone whom I’d known as this liberal, compassionate, rational Conservative ended up making arguments about Turkey (joining) and being swamped and what have you.
"They were trashing the government of which they were a part, effectively."
Responding to David Cameron's comments, cabinet minister Nicky Morgan has said "I don't think it's actually very helpful to keep rerunning the 2016 campaign and who said what, when."
She added: "The fact is, we had a result and actually it's incumbent on those of us who are in government, still MPs to make sure that result is delivered on."
She told ITV News she would vote to remain in the European Union if given the chance in a second referendum.
"I have been very clear and much to the surprise of people today that I would vote to remain but actually I don't support a second referendum," Ms Morgan said.
She added: "I think we've had a result in 2016 and it's now incumbent on MPs in parliament to make sure that result is fulfilled."
"I would much prefer to leave the EU with a deal, that is the government's stated preference too but we have to be ready that in case a deal can't be struck."
The Culture Secretary insisted she did not support holding another poll and believed the original result needed to be "fulfilled".
Mr Cameron, who said the Leave campaigners "left the truth at home" regarding Turkey joining the EU and the claim Britain sends £350 million a week to the EU, also criticised Priti Patel’s "attack that wealthy people didn’t understand the problems of immigration".
He added: "It felt very like she was put on point to do some attacking of the government and its record.
"I suppose some people would say all is fair in love and war and political campaigns."
He added: "I thought there were places Conservatives wouldn’t go against each other. And they did."
He also revealed that he once texted Mr Gove, now Chancellor of the Duchy of Lancaster, to say: "You are either a team player or a w*nker."
The former PM – who admitted to being "hugely depressed" about leaving Number 10 – said Mr Johnson was "easy to work with" but admitted there had been "issues" between the pair.
Mr Cameron said: "I want him to succeed. I worked with him well, as I say in the book. I also say that he was a capable mayor.
He added: "He was easy to work with. I thought he was very talented. I wanted him in my government."
He continued: "We’ve had issues. Even before Brexit, there were sometimes tensions and disagreements but, on the whole, we’ve got on well. And I want him to succeed.
"Look, he’s got a very clear strategy and plan. It’s, you know, not the approach that I would have taken, but I want him to succeed."
But on Mr Johnson’s recent decision to prorogue Parliament for five weeks and withdraw the whip from 21 Tory MPs – including the likes of Ken Clarke and Sir Nicholas Soames – Mr Cameron expressed his disapproval.
"Taking the whip from hard-working Conservative MPs and sharp practices using prorogation of Parliament have rebounded. I didn’t support either of those things. Neither do I think a no-deal Brexit is a good idea," he said.
David Cameron's first in depth television interview about his time in office will be broadcast on ITV on Monday 16th September at 8pm