This office wouldn't be much of a challenge for Through the Keyhole. The walls are plastered with photographs of David Frost chatting to stars and statesmen – Bobby Kennedy, Sammy Davis Jr, George Bush Sr, Bill Clinton, Paul McCartney and George Bush Jr and we've barely started. In one corner is a framed Private Eye cover of Frost and Tony Blair under the headline "Blair Admits Iraq Disaster" – the bubble from Frost's mouth says "You just told the truth"; Blair responds, "It was a slip of the tongue." In another corner is a bust of Frost wearing a dirty pair of glasses. The coffee table carries DVDs of highbrow Frost (his interviews with Richard Nixon) and low-brow Frost (DVDs of Through the Keyhole, the TV celebrity guessing game he presented for more than 10 years) and a copy of the David Frost autobiography Part 1 (542 pages, and again we've barely started). I ask his assistant what he likes to be called – "Sir David," she says instantly.

Frost enters the room with a gust of can-do energy. He doesn't quite say "Hello, Good evening and welcome," but almost. He shakes hands and tells me how very, very pleased he is to see me. "How long have you been with the great Guardian then?" "Twenty-one years," I say, feeling every inch the office junior. He claps his hands with delight. "No! Studio applause!" Frost is famous for his charm. He still speaks in that unique way – every word absurdly stressed and accompanied by a nod of the head.

The presenter/journalist/satirist/producer/businessman/you name it is 72 now, and has no intention of slowing down. If anything, he's had a new lease of life since the film Frost/Nixon (based on the play) came out three years ago. In September the BBC will pay tribute when it screens Morgan's film along with the classic 1977 Watergate interview, and Dame Joan Bakewell will interview him. He presents his weekly show on Al-Jazeera, is finishing off a television programme about the art of interviewing and has just embarked on a career as a clothes horse for Dunlop. "It's only 50 years since I started in television, so there's many more years to come," he says in the press campaign, underneath a suave photo of him in DJ and dickie bow. "Being upbeat is the key to life."

It really is the key to Frost. He grew up believing he could do anything. His Methodist minister father and housewife mother had little materially, but instilled in him a tremendous self-belief. A grammar-school boy, he went to Cambridge to study English. By then he had already discarded careers as footballer, teacher and preacher. How good a footballer was he? "Well, I suppose good enough … when the scout came from Nottingham Forest it was to watch somebody on the other side, so that day I was hot stuff." How many did he score? "Eight. The final score was 8-1, or 8-2." In the end, he was too ambitious to become a footballer. "The maximum wage in those days for a footballer was £20 a week. If Sir Stanley Matthews took a penny more, he'd be suspended for life."

And that put him off ? "Yeah, I think it did. There was no financial incentive to becoming a professional footballer."

From 18, he worked as a lay preacher at the local Methodist church for two years. What was the most important message he wanted to get across? "John 3:16 is at the heart of it isn't it?" Which is? "'For God so loved the world that he' … I'm trying to remember … 'sent his only son to die ... " Frost leaves the room, and heads for his PA. "Have you got a New Testament?" he asks her.

"I can check online." He bounces back in to the room. "An unusual request!" How did he go from preacher to satirist? He slaps his coffee cup on the saucer a little harder than intended.

"It is a mix, isn't it?" he says, as if he's considering it for the first time. "I'm trying to think of the common thing between the two ... if you're interested in reform, in changing things, that is consistent with parts of the Bible, isn't it? There were even a few jokes in my sermons at the age of 18."

His PA returns with a scrap of paper. "Ah, that's it," he says with delight. "For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life." He pours another coffee.

By 23, he was presenting the TV satire That Was The Week That Was. Before long, he was dividing his working week between America and England, in the process becoming Concorde's most frequent flyer. "I'm not driven, I'm flown," he once said of his ambition. He loved America, where aspiration was seen as a positive rather than something unseemly. Anyway, he says, he never regarded himself as unhealthily ambitious, it's just that there we so many things he wanted to do. "I think it links in with that thing which people say is very Methodist, or puritanical – we have a duty to use whatever time and talents we have to the full." Did that come from his father? "Yes, that's Dad. And also from Dad was the proverb 'Even a stopped clock is right twice a day', which is a great quote, because it says everyone has got something to teach you if you make enough effort to find it."

He sits squeezed tight into his Le Corbusier chair, stitching his life together with anecdotes of the rich and famous. There's the honour of George Bush Sr, who promised him his first interview when he won a second term, and was true to his word; the extravagance of Sammy Davis Jr, "who took off his diamond watch and gave it to me" after a show; his combative relationship with Lady Thatcher, who called him "bonkers" on air and berated him off air for feeling guilty about using private healthcare ("she said, 'how could you of all people say that, Mr Frost? It just shows how socialism has pervaded this country!'"). He's wearing a huge blue tie that dangles halfway down his thighs, a blue striped shirt, blue suit, and trademark red socks and braces. He looks super stylish from a distance, and slightly unkempt close up – his fingernails are long, his glasses smudged, and there are stains on the suit. His hearing aid rests deep in his ear, and his hands shake a little as he talks.

In the 1960s and 1970s, David Frost became a global phenomenon. He was never off the TV, whether mingling with the stars or interrogating prime ministers and presidents. He soon became the butt of the very satirists he had grown up with. They seemed to regard his ambition as undignified and unBritish. Peter Cook accused him of nicking stuff from him, and labelled him "the bubonic plagiarist". A story emerged that Cook had said one of his great regrets was saving Frost from drowning. Frost is still sore about this, and says it's simply not true. "That wasn't Peter's line, that was Alan Bennett's joke." So there was never any conflict between him and Cook? "We had a period of rivalry when he was in New York doing Beyond the Fringe and I was in England doing That Was The Week That Was. And of course, if you are specialising in satire, as we were, it ill behoves you to complain about satirical jokes being made about you." The thing that seems to pain him most is the idea he was disliked. "Private Eye had a year where they did a fair bit around me, but that all faded, too. I don't know anybody who really behaved like an enemy." He pours another coffee. I've never seen anyone knock it back like he does. So Cook didn't stop him from drowning? Oh no, he says, that's absolutely true. "It was 1963 and I was staying with Peter in Connecticut. He said, 'I thought David was doing a satirical attack on drowning, but then I realised it was for real, and I thought I better rescue him because with our rivalry at the time people would probably think I'd pushed him in.'"

Of all his achievements, one stands out. His gladiatorial contest with Richard Nixon is perhaps the greatest television interview ever. It's not simply the mea culpa he extracts from the US president over Watergate, but the scale of the project (29 hours of conversation, edited down to six), the risk (he sold his shares in London Weekend Television to pay Nixon $600,000 – it was regarded by many as the start of chequebook journalism), and the drama (the real thing is even more compelling than the movie).

Why was he willing to sacrifice so much to get Nixon? "He was the most interesting person to interview in the world." Did he think this was his grasp at journalistic immortality? He laughs. "Well, no one would ever admit grasping for immortality … I suppose one hoped the interviews would make history in some way, as a document on the Nixon presidency. So that was the ambition, obviously. Also one hoped they were bloody good television."

There is a moment in the interview when you can almost smell Frost's relief. Does he know which bit I mean? Frost smiles, and quotes it back to me as he might have recited the bible to his congregation all those years ago. "We'd got through to the 'I have to live with that for the rest of my life, I have let down the American people … " But the thing Frost remembers best is an exchange at the very end, with the cameras turned off. "I said something to him like, I think we've not so much been through an interview as been through a whole life, and he said, 'Bit tough for you was it?' – which was so Nixonian; that the person who was really under pressure was me, not him.' He laughs to himself, and takes another slug of coffee. "Bit tough for you was it?" he repeats to himself.

I recently read that Frost was worth around £200m. Is that true? He seems to be working it out in his head. "No, I shouldn't say so. It's not as much that. Depends which currency. In yen, perhaps. I would say five figures rather than six."

Surely he mean eight figures rather than nine? He takes out a pen and pad and scribbles down an imaginary figure – £40m. "Yes I was thinking thousands wasn't I? I think you're right – eight figures rather than nine."

Frost has his critics who say he got too close to the establishment (his three sons with Lady Carina went to Eton), was a sucker for celebrity, and that his interviews were too soft-focus. There may be some truth in this, but he has kept a hunger for the scoop (he's desperate to get Obama to complete his clean sweep of presidents in his time). When he went to Al Jazeera he was thought past his sell-by date. But he says it has been a great experience and opened up his world view. "When Al Jazeera English started five years ago, it was 50 countries and 80m households, and now it's 125 countries and 250m households, which is fantastic." He pouts triumphantly, like a boxer who has ducked a savage blow. More coffee. He says he has not received a single editorial directive in all that time "It came along at the right moment. Breakfast with Frost had just ended and this was a terrific new challenge, and I thought it was probably the last major new news network the world would see."

What if the BBC or ITV came back for you? He thinks about it. "At this moment in time – which I think was actually a Nixon phrase – " He distracts himself with yet another anecdote. "Al Haig, whose English was even more convoluted than Nixon's, once said in an interview, 'at this juncture of maturation'." He realises he's lost his track and glugs another coffee (his sixth, by my count), spills some on his shirt, dabs it away and continues. "Oh, it's all right. It will dry. So where were we? Oh yes, I'd have to say, 'That's great, but for the time being it may be difficult to fit it in ... But I'm sure love will find a way'." And his lips pout again before creasing into a smile.

• This article was amended on 4 July 2011. The original referred to Al Hague. This misspelling has been corrected.