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TW3 was only on air for eight months before being halted in December 1963, not least because of the furore that erupted over a sketch I had written for David, in which he impersonated Benjamin Disraeli attacking the new Tory prime minister, Alec Douglas-Home.

But in January 1964, the cast and writers of the programme we had put together the day after President Kennedy's assassination, were flown to re-enact it in front of 50,000 people in New York. I had never seen David as starstruck, sitting in his hotel room transfixed by the top American talk shows, which in those days were the very furnace of the modern celebrity fame created by television.

The following winter, we worked together again on a laborious sequel to TW3 which, over three nights of a weekend, tellingly tried to mix sketches with a Frost-centred talk show. But it never really worked, and in 1965 the BBC sacked him. For months he was at a low ebb, until in January 1966, he pulled off the masterstroke that was to relaunch his career. He invited an array of famous names to breakfast at the Connaught Hotel, headed by the prime minister Harold Wilson (who only accepted because he was told, untruthfully, that one guest would be Paul McCartney).

David had intuitively recognised what Daniel J Boorstin meant when he wrote in his book The Image of how "being well-known for their well-knownness, celebrities intensify their celebrity images simply by being known for their relations among themselves. By a kind of symbiosis, celebrities live off each other."

I then watched from a distance as "the man who had invited the Prime Minister to breakfast" embarked on that dazzling series of moves that, within four years, were to give him his own talk show as a "fearless interviewer"; his own television company centred on a five-nights-a-week chat show; and, simultaneously, three nights a week on screen in America, engaging in glutinous chat with the starriest galaxy of celebs money could buy, and being hailed as "the best-known Englishman since Winston Churchill".

It was around then that, when I was discussing him one day with Malcolm Muggeridge, Kitty Muggeridge chipped in with her immortal line: "I suppose you could say that Frost has risen without trace." He seemed to have vanished into a kind of televisual cyberspace, never more obviously than the dream-like moment in 1974 when, on one channel, he was in the Congo, after Muhammad Ali had just won a world heavyweight fight, with a diminutive Frost on the edge of the screen shouting "Super, Muhammad, super", while, switching to another, we saw him cosying up, knee-to-knee, with Teddy Kennedy, saying: "It's a joy to be with you again, Senator."

Never again was he to enjoy such starry prominence as in those few brief years, when he was inflated into the most extraordinary phenomenon in television history. Both in America and Britain, his star waned, and though he was building his lucrative business empire, it was as a last gamble to save his television career that, in 1977, he signed up the disgraced former president Nixon for those interviews that became the most famous thing he ever did.

It was to mark that gamble that I wrote my critical appraisal of Frost as "the man who rose without trace", observing that only in the age of television could a man of such limited talents have risen to such prominence. All the guises he adopted along the way – cabaret artist, satirist, fearless interviewer, intimate of the stars – were merely means to furthering the distilled purity of his ambition to become famous just for being David Frost.

I added, however, that it was wrong to see him as just an ordinary person blown up large by the media. David did have unusual gifts – superhuman energy, compelling charm, an extraordinary memory for faces, great personal generosity. But the bad fairy at his christening decreed that all these should be used to serve only one end, to become world-famous simply for being world-famous.

What did it all really add up to? During the height of Frost's fame, I asked the Nobel Prize-winning economist Frederick Hayek what he made of Frost. "Frost?" Hayek replied. "I've never heard of this man."

But now that the lights have gone out and the dream fades, I can remember "Sir David", as many others have been doing, only with amused but genuine affection – for the warmth of his unfailing geniality, and as one of the most extraordinary people I have met on this earth.