Huddled in the corner of a BBC cafeteria nursing soft drinks, they look like any other devoted couple of oldies. They call one another “dear”, they finish each other’s sentences.

But they are not typical OAPs. He is a sir, and she is a dame. He shared a stage with Charlie Parker in 1949 and played alto saxophone with everyone who mattered right up to doing Jools Holland’s show with Craig David. She conquered America with her singing – not just jazz, but opera and lieder, too – and starred as an actress in London, New York and LA. And, while we are not quite talking Cliff Richard, they look much younger than their years. Both will be 80 in the autumn.

John Dankworth and Cleo Laine have just been on BBC Breakfast plugging their Proms show, From Bards to Blues. Laine set the alarm for 4am – they live in genteel splendour in Wavendon, Buckinghamshire. Her husband says that he was never sure whether this newfangled breakfast TV was worth the dawn start. But when he was in America he came across an elderly Bob Hope in an early-morning studio and thought, “if he thinks it’s worth the effort, then . . .”

Their Prom will celebrate Shakespeare’s link with jazz. This may sound tenuous, but there is an honourable tradition of jazz works inspired by the Bard – from Bernstein’s West Side Story through to Duke Ellington’s Such Sweet Thunder (musical portraits of Shakespearean characters) and Dankworth’s settings of sonnets for Laine on the album Shakespeare and All That Jazz. Many consider this 1964 LP the pair’s masterpiece; some of the settings will be on the Prom bill, as will the Ellington.

Shakespeare has a special appeal. “Often when you read it, there is almost no composition to do. The intonation suggests the tune,” he says.

“His stories lend themselves,” adds Laine, “and the language rolls off the tongue. And of course if you’re the composer [she smiles at her husband], he doesn’t answer back.” The Shakespeare album was used in schools to introduce students to his language. “There are lots of people all over the world who say that the first time they heard me was their teacher playing something from that record.”

Is Laine still surprised to be getting up on stage to sing it four decades on? The jazz life isn’t famous for longevity. “We certainly didn’t participate in the heroin kick like Charlie Parker and a few others,” says Laine. “I’ve lasted because I’m in a style of music that doesn’t die.” Pop stars will find it harder – though she’s impressed by Mick Jagger, who, the pair assure me, learnt many of his moves from watching their late friend George Melly.

Laine began singing seriously in her mid-twenties, joining Dankworth’s band in the early 1950s and then marrying him. “He thought that he was getting a cheap singer, but he got an expensive wife.” They didn’t play in America until 1972, but success was almost immediate. Laine was the new queen of the high Ds (yes, that is one up from the opera diva’s C). Dankworth can still quote from The New York Times review of their first show: “The British, who have been bombarding us with rock bands, have been hoarding one of their national treasures.”

Why do they keep going? Because they love what they do. Dankworth is still composing – he has just finished The Blues Ain’t, a song cycle of “unlikely blues songs” that will also feature in the Prom. Laine declares that the orchestration and band parts are outstanding. She pats his back: “You have excelled yourself, sire.”

It’s time to go: Laine back home to put her feet up, Dankworth across town to rehearse for the BBC Jazz Awards. An aide tries to pick up his saxophone case. “I’ll take that,” he insists. “You wouldn’t see someone carrying Federer’s racket for him at Wimbledon.”

That night he presents a lifetime achievement award at the Mermaid Theatre in London to the pianist Dave Brubeck. It’s a chance for Dankworth to play the young pretender – Brubeck is still performing at 86.

From Bards to Blues, Royal Albert Hall, Kensington Gore, London SW7 (www.royalalbert hall.com 020-7589 8212), Wed

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