Now that the plaudits are rolling in for Alan Bennett's play The Habit of Art, which imagines a meeting between Benjamin Britten and W H Auden, perhaps Bennett should turn his attention to another meeting that never was. By an extraordinary coincidence, four of Britain's best-known public figures all grew up in Liverpool at around the same time.
It is easy to imagine the opening scene - a church fete, perhaps, somewhere in Liverpool, say in 1957 - but impossible to imagine where things might go afterwards. Apart from a shared but ultimately juvenile interest in that vanished fad of the late 1950s, rock'n'roll music, Paul McCartney and the future Lord Lennon had virtually nothing in common. And even if they had got together with those two other distinguished Liverpool boys, Richard Starkey and Sir George Harrison, their lives are now so different that you wonder what on earth they would have talked about.
One conceit might be to imagine them setting up some kind of skiffle group; after all, Lennon was once a member of a band called the Quarrymen, while the others, like all teenagers of the day, were interested in pop music. The problem, though, is that skiffle was such a musical cul-de-sac, and rock'n'roll never had the variety and depth to survive. As Decca's Mike Smith, music's most celebrated talent-spotter, remarked in 1962: "Groups with guitars are on the way out." The future lay with trad jazz, the ancestor of 21st-century genres such as death jazz, trad punk and hop hip. Acker Bilk was always going to be a star; John Lennon never was.
Instead, our four youngsters ploughed very different furrows. With his Liverpool background, Starkey was perfectly placed to profit from the kitchen-sink drama boom of the early 1960s. He became the symbol of the British New Wave, his acting skills taking him from the Royal Court theatre to six Oscar nominations.
As for Sir George, from an early age he displayed the love of money that made him a household name in the 1980s: the man who brought Indian ready-meals to the ordinary family, the most notorious of all Thatcher's corporate raiders and the star of the BBC's The Apprentice.
Meanwhile, Lord Lennon remains one of the most recognisable figures in British public life, although it is seven years now since he stepped down as an unusually sanctimonious Archbishop of Canterbury (catchphrase: "Nobody is more popular than Jesus"). And Paul McCartney - oh dear. With his affable manner and easy charm, he was always one of the easiest Tory MPs to like, but the expenses scandal - a second home on the Mull of Kintyre! - really did him in. Perhaps he should have joined a band after all.