Its four performers were Cook, Alan Bennett, Jonathan Miller and Dudley Moore. The contrast in their careers is famous and familiar. Moore went to Hollywood and Cook has now gone to the great beyond, both to some extent unfulfilled. They were the pure comedians of the quartet.
The other two were the intellectuals, Bennett having been a medieval historian and Miller a medical scientist before they both forsook academic life.
Bennett is not only one of the most successful playwrights of his time, but seems to have taken over from Betjeman as the nation's literary teddy bear.
As for Miller, you can scarcely talk of his "career" since he has had several: neurologist, comic actor, television director, author, populariser of science. But most of his time and energy for 25 years has been devoted to theatre production, the dramatic stage to begin with, but then increasingly - and in the end exclusively - opera.
The list of credits is dazzling, from his early days with Kent Opera, to Glyndebourne, English National Opera, to the Met in New York and La Scala in Milan. Now he has made a belated debut at the Royal Opera House with a new production of Cosi fan tutte,coinciding with another revival of his famous mafiosi Rigoletto at the Coliseum.
Yet Jonathan Miller at 60 is fed up - famously, noisily, angrily fed up. He is fed up with journalists, he is fed up with critics in particular and he is fed up with Britain, its philistinism, its insularity and its habit of denigration. And he knows howto say so. He likened Margaret Thatcher to typhoid, and of journalists he once said: "I get annoyed that some pipsqueak is allowed to publish his used toilet paper. I know what I'm doing better than they do."
The opera establishment is not spared. One opera house management was "the Ceausescu regime", opera singers are "dim-witted celebrities" who are "buggered if they are going to do any smart- arsed idea that you've got as a director". And a large part of the audience are "disgusting old opera queens".
Twice, at least, he has been so outraged at this country that he has publicly threatened to leave it.
Jonathan Miller was 26 when Beyond The Fringe first appeared at the Edinburgh Festival - the year before it opened in London. Although he doesn't think he was a very happy child, he came from a comfortable home: his father was a neurologist and his mother a novelist.
One of the memorable lines from Beyond the Fringe is Miller saying he wasn't a Jew, actually, "I'm Jew-ish - I don't go the whole hog." This is quite accurate. He has no connections with Jewish life.
All the same, he was pigeon-holed as a clever Jewish boy at St Paul's school along with his friends, bookseller and columnist Eric Korn and Oliver Sacks (who wrote The Man Who Mistook His Wife For a Hat). Sacks remembers the tensions and overtones of schooldays when the clubs they organised would be banned for no apparent reason.
Miller went on to Cambridge to work at medicine and play with Footlights, making his name as a brilliant clown. Even before he speaks there is something irresistibly funny about him on stage, angular and gawky, like a stork which can't quite take off. Inan early phrase that may have prompted his first irritation with critics, he was "the English Danny Kaye".
But he stuck to medicine until the day in 1960 when John Bassett, an ingenious impresario in charge of the Fringe at the Edinburgh Festival brought together four gifted graduates for lunch at an Italian restaurant in London. Four years later they were playing in New York and, in quite different ways, they have never quite got the greasepaint off.
Miller's first departure was television. He joined the BBC as an editor of the arts programme Monitor; he directed Alice in Wonderland; he interviewed Susan Sontag. It is easy to date from this point a new reputation and a new antagonism. The funny man had turned serious, the clown was playing Polonius - and Miller was cast as a pseud.
Private Eye started a "Dr Jonathan" column, pastiching Boswell, and went on running it when they found how much it upset Miller.
He returned to his first vocation as a research fellow in the history of medicine at University College London, but not for long (though he has since held academic posts in California and at Sussex). He made a television series, The Body in Question, which a fairly friendly critic called "a gloriously manic mixture of all those things to do with the human body that happened to appeal to Dr Miller's fertile mind".
But he was soon back in the theatre. From 1973 to 1975 he was an associate director at the National but that ended in a very stormy falling-out with Peter Hall, and his directorship of the Old Vic ended when the angels ran out of money. For all that, he seems never to have been short of work since.
So what is eating Jonathan Miller? On any objective view the man should be counting his blessings. Regular work and prosperity apart, he has been married to Rachel Collet, a GP, for 38 years. They have three children and by every account a happy marriage. Miller also has a number of devoted friends, Bennett, George Melly and the cartoonist Nicholas Garland among them, and, for a man of his temperament, remarkably few personal enemies (as opposed to professional antagonists).
As for English philistinism, it is a fact of life which others seem able to bear. Of course the bluff, blokey insularity that dismisses most of European culture as pseudish or boring is as depressing as the weather, but this is hardly the dominant tone of cultural life.
Miller does indeed come close at times to saloon-bar paranoia. One of the most audible people in the country, he talks as though nobody ever listens to him. Certainly there is something odd about his long absence from Covent Garden - the one piece he wasoffered there was La forza del destino, which was "like being invited to defuse an IRA car bomb". But it doesn't end there. Glyndebourne, he says, "has been closed" to him for 20 years. The Welsh National Opera never used him because "you had to be Romanian or Albanian or East German". And he even detects something malign in the way in which he is so often described as "Dr Miller" and "the good doctor" - detecting, perhaps, a suggestion that he should have stuck to medicine.
What are the grounds for all this? His productions have been successful and usually well-praised, including Cosi (one of the more enthusiastic notices referred to him as "the good doctor"). In any case, as the pub bores say, it's a free country. Why shouldn't critics like some of his work more than others? He is hit and miss. His Rigoletto with mafiosi was clever and worked. His Tosca updated from Napoleon to Mussolini did not.
He loathes the idea of being treated as a clever undergraduate, but it is precisely his enthusiasm which can be infectiously enjoyable. A friend remembers staying in the same house in the country years ago when Miller was directing Cosi for the first time. As he perused the libretto, he suddenly exclaimed: "It's Mansfield Park!", at which they all had to go to the nearest town to find copies of the novel (and never mind that it isn't Mansfield Park).
Behind all the anger seems to lurk some sort of frustration or disappointment. The greater part of Miller's working life has been spent as an opera producer, which the late Hans Keller used to class as a "phoney profession" - one which did not formerly exist, and whose invention created more problems than it solved. Miller might not agree, but there are hints that he is oppressed by the transience of what he does, a fear that none of it will be remembered.
Is he a great scientist manque? A doctor who admires him points out that the Fringe years hopelessly interrupted his medical career. "As a student you learn a basic vocabulary and grammar. What matters are the years after when you learn to use them", which was just what Miller missed. Neurology is rather like professional tennis or football; you can't take five years out in your 20s and then return to the game at the same level.
Not becoming a great original scholar shouldn't prevent him becoming a great populariser, rather the contrary, but he has done less in this line than he might, just The Body in Question and a series on the history of madness.
He once told an audience of television people that their medium was "important because of its utter banality". Banal Miller is not, but he is made for television and he should do more, a series, perhaps, on the history of opera, or art, or medicine, or comedy.
Miller may have missed his original metier, but 60 is a ripe age for a polymath to find another.