Jeff Beck, the rock guitarist, was making a surprise appearance at the Proms last night — and creating a piece of musical history.

Beck, 64, who made his name with the Yardbirds in the 1960s, was due to play a guitar solo during a late-night concert of jazz and blues organised by Nigel Kennedy, the violinist. The two men have got to know each other over the past few months through a mutual love of jazz.

Kennedy, best known for his Vivaldi and Elgar renditions, invited Beck to join him in the Albert Hall. “It’s monumental to be playing at the Proms,” said Beck shortly before he was due on stage.

It is the first time a genuine rock star has played at the 113-year-old festival even if the Proms, which are mainly a celebration of classical music, have on occasion broken the mould with performances by Michael Ball and Ravi Shankar. Soft Machine, the avant garde jazz-rock group also played a Prom in 1970.

Beck, however, is a genuine rock legend who replaced Eric Clapton in the Yardbirds. He had a solo hit with Hi Ho Silver Lining before leading his own group with a young Rod Stewart and Ronnie Wood, to whom he bears an uncanny resemblance. In the cult 1966 movie Blow-Up, Beck breaks his guitar — a scene replicated in the spoof rock documentary, This is Spinal Tap.

“I’d long admired Kennedy both for his classical music and his jazz,” said Beck, who for 17 years lived with the 1960s model Celia Hammond, now better known for rescuing stray cats.

Last night Beck, who has won four Grammy awards for best rock instrumental performance, played a jazz number, Hills of Saturn, composed by Kennedy. Earlier in the evening Kennedy had performed Elgar’s Violin Concerto before coming back on stage with his own quintet, formed in Poland where he now lives for half the year after marrying a Polish woman.

“Nigel was particularly keen for me to do the Hills of Saturn solo,” said Beck, who played the track on his Fender Stratocaster electric guitar.

Beck’s career has had its ups and downs, although he says that he has few regrets — not even turning down the chance to join the Rolling Stones in 1974.

“I was asked over to Amsterdam for an audition after it was clear that Mick Taylor was leaving the band,” said Beck, who also played with Jimmy Page in the Yardbirds before Page formed Led Zeppelin.

“But I got fed up waiting for the audition. Anyway, I would not have liked all those girls and booze that the Stones were associated with. Also I had a better offer — for George Martin to produce an album of my work.” That album, Blow By Blow displayed Beck’s technical prowess in jazz-rock.

Beck laughs at his association with Clapton. “People always link us,” he said. “But we are very different and play very differently.” However, the two keep in touch with Clapton turning up to see Beck play recently at Ronnie Scott’s jazz club in central London.

The rock star, who lives in East Sussex where he spends much of his spare time restoring American hot-rod cars, is particularly glad to have played with the Yardbirds because, he says, they were not a pop group but a band that tried all sorts of music.

Kennedy was delighted at his coup of getting Beck to play. The maverick violinist was making his first performance at the Proms for 21 years after falling out in the early 1990s with Sir John Drummond, then director of the Proms. Kennedy, now 51, still despises Drummond, who died in 2006.

In fact Kennedy has his knives out for the classical music Establishment. “Classical music itself is beautiful, but not the bureaucrats who run the industry. They stifle invention. It’s an incestuous world where the women are still in old Laura Ashley dresses and the men talk about their old school, Eton,” he said.

Last night Roger Wright, director of the Proms, argued that Kennedy’s jazz music and Beck’s solo were “part and parcel of the wide agenda of music of the Proms”.

Asked if Sir Henry Wood, the founder of the Proms, would have approved, Wright commented that Wood always sought out new music.

The Royal Opera House has a longer history of welcoming rock musicians. Björk, the Icelandic singer, performed there in 2001; Motorhead shouted the house down in 2004. And an opera called Monkey by Damon Albarn, formerly of Blur, is a sell-out for its evening performances at Covent Garden this week.

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