Desert Island Discs’s antiquity is such that its first castaway, in 1942, was a Viennese comedian who had fought alongside his fellow Austrian Adolf Hitler in the first world war. Despite that uneasy conjunction — delicate in a country that at the time was fighting Hitler — the programme’s creator Roy Plomley was unperturbed.

He conversed in a bomb-damaged Maida Vale studio with the comedian Vic Oliver in the cosy and above all collaborative manner that became his hallmark for the next four decades, during which he sent Princess Margaret and 1,700 others off to his mythical isle and made it a national institution.

So when the BBC said tartly in 1989 that the show was “no longer an honours list” (thereby seeking to justify its invitation to Lady Diana Mosley, widow of the British Union of Fascists leader Sir Oswald Mosley), it could not have been more wrong. That is without doubt what it was, is and still will be when Kirsty Young takes over.

A one-way ticket to the island is a badge, if not of universal acclaim then certainly of general approbation. That is why so few turn it down (they include GB Shaw, Laurence Olivier, the Prince of Wales and John Prescott). Similarly, to host it is to occupy one of broadcasting’s most coveted posts.

“If I had felt honoured at being chosen as a castaway, I felt ennobled when I was told that the job of presenting it was mine,” recalled Sue Lawley in her book on the programme. She will have transported some 750 guests, including Gordon Brown (“people want to know whether you’re gay”), Joan Collins, the Archbishop of Canterbury and the Duchess of Kent by the time she leaves on August 27.

The programme is not an unchanged survivor from the era of Bakelite. Those who appear on it expect now to be interviewed, not massaged. Luxuries were allowed only from 1951 and have included an inflatable rubber woman for Oliver Reed, a stick of the finest marijuana for Norman Mailer, an oriental cat for Princess Michael of Kent, a Plasticine figure of Plomley with a supply of pins for that strangest of men, Jeffrey Archer; and, rather sadly, a revolver for Artur Rubinstein and liquid Temazepam for Nigella Lawson as an exit from unbearable solitude.

Books were introduced only around 1960, enabling the immodest Otto Preminger to take his autobiography and George Clooney to opt for War and Peace “because there may not be toilet paper . . . and it’s a huge book”.

The essence of the show has not changed: eight records to spend the rest of your life with, topped and tailed with herring gulls and Eric Coates’s By the Sleepy Lagoon. The wonderful simplicity of that formula holds the key to the programme’s success.

It is a slightly deceptive simplicity, because the records — usually music but not always — involve choices that reveal emotion and character. All but one of Elisabeth Schwarzkopf’s selections were her own recordings, while Margaret Thatcher asked for Bob Newhart’s comic monologue Introducing Tobacco to Civilisation.

“Music alone cannot make the island attractive,” wrote Lawley. “It is people’s thoughts and observations related to their music which do that.”

Thus the scepticism sometimes voiced about politicians and the suspected influence of spin doctors. Why did Tony Blair and Iain Duncan Smith both pick Bruce Springsteen? Conceivably because both sought to be cool. David Cameron, heir to Blair, wants to be even cooler, hence his Killers, Smiths, Radiohead, and so on.

Anyway, they fit that brilliantly simple formula which Plomley, then a compere and writer, suggested in a letter to the BBC. One cold night in November 1941 at his digs in Hertfordshire his fire had gone out and he was already in pyjamas. “Nevertheless, I sat down at my typewriter,” he recalled in his first book, “and wrote to Leslie Perowne, who was in charge of the lighter kinds of record programmes.”

Because Plomley was a freelance, Desert Island Discs became his copyright. After his death in 1985 it went to his wife, Diana Wong. She still owns it but is now in her eighties and their daughter, Almond, acts for her.

Mother and daughter and the BBC agree on the need to have Plomley mentioned in the credits and the corporation pays Diana an annual sum (£5,000 in 1996, so probably more now). However, the family and the BBC cannot agree on the availability of the show after its weekly broadcast. This is why it is not available to listen to via the BBC’s website. Anybody hoping for that is greeted with this terse message: “For rights reasons, Desert Island Discs is not available as a listen again item.”

Wong has not been slow to assess her late husband’s successors. She was sharply critical, as were others, of Michael Parkinson’s two-year stint (1986-87). About Lawley she has been more muted, though famously remarking after the Brown edition that she demonstrated “an extraordinary obsession with other people’s sex lives”.

Young, who will be the fourth host of the show in its 64-year history, will have a hard act to follow, for at her best — neither coquettish nor frosty, neither intrusive nor fawning — Lawley has been superb. My eyes mist over even now, almost 17 years after it went out, at her sensitive treatment of the pianist John Ogdon, who described how his therapy for mental illness had involved the baking of sponge cakes.

Desert Island Discs is of course a list, and people love lists. It is a game, although not one played against others. But above all, if taken sufficiently seriously by the guest, it is about one life and the music flowing through it — music that touches a chord, recaptures a moment, offers solace, comfort, meaning and happiness. There is no reason why it should not go on for ever.