The 66-year-old revealed in the latest episodes of the fifth season of his series Clarkson's Farm that he had been diagnosed with "aggressive" prostate cancer that had been discovered early.
In an interview with The Times, Clarkson confirmed that a PSA test two months ago revealed no indication of cancer and he is officially in remission.
"I was talking to David (Cameron) about it earlier this morning," Clarkson said.
"He said the amount of people that come up to him mostly in public conveniences and say, 'if you hadn't owned up to it, I wouldn't have got checked, and they wouldn't have found it"."
"So now there's a group of us, (food writer) Giles Coren, David, me, one or two other people, and we meet for lunch every so often. Everybody has different Gleason scores, and everybody has different Stockholm and PSA scores. We all compare notes and I actually get muddled with what mine were.
"But it is quite funny watching people looking at us and going, 'that's quite an interesting group of people, what do they all share in common?'."
Clarkson went on to say that the news of his diagnosis has "landed harder than I thought it would".
He added: "This is why I have to say to everybody who's reading this, please, please, please go and get checked.
"It's not uncomfortable, it's not undignified and it's a no-brainer. I did, and that's why I'm sitting here talking to you 11 months down the line.
"I've seen so many people die of cancer. It doesn't bear thinking about what it must be like to live knowing that an illness is going to kill you.
"It must be very, very, very distressing. I don't know the history of what happened to (former Olympic cyclist) Chris Hoy but to be told your cancer is inoperable and to still carry on you'd have to be incredibly brave."
Speaking from a hospital bed at the end of the season finale, Clarkson revealed he had experienced complications during treatment, which he told The Times had been caused by him resuming a course of tablets he had been taking for his earlier vascular and cardiac problems.
He said: "That was horrific and it was all my own fault. I'd been on drugs for heart issues and I had to come off them during the cancer treatment.
"Two or three weeks after the cancer operation, I thought I'd better put myself back on those blood thinners. Big mistake, huge.
"It (resulted in) a very big emergency in the middle of the night. I'm not even going to go into the treatment that was required as a result of that, because it was horrible. I didn't ask a doctor, I just thought, 'I'm sure it will be all right to go back on blood thinners'."
The diagnosis came almost two years after Clarkson underwent a heart procedure in which he was fitted with two stents to improve blood flow to the heart.
He said his doctor had told him to stop working following the operation and that he had been advised to replace work with golf in a column for The Sun at the time.
The TV presenter previously quit smoking after contracting pneumonia on holiday in Spain.
Clarkson's Farm follows the long-time television presenter and his crew as they navigate the challenges of running Diddly Squat Farm near Chipping Norton, Oxfordshire.
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