It’s 22 years since I first met Nigel Kennedy, but some things never change. Instead of a handshake we have the mandatory clash of knuckles. “Ooh, very hip,” I say. “And more hygienic, man,” he replies.

Equally obligatory is ten minutes of heavy-duty football talk. Even at 51, Kennedy takes his footie as seriously as any other overgrown adolescent. This is the man who once had his Jag painted in the claret and blue of his beloved Aston Villa. When I arrive at his North London home (his second home, now that he’s settled in Poland with Agnieszka, his young Polish wife) his PA is copying all of next season’s Villa fixtures into his diary. After that, presumably, she’ll have to repeat the task for Cracovia, his adopted Polish team. “Most important thing you’ll do all day, darlin’,” he says.

The formalities over, we settle down to serious talk about music. Which, with Kennedy, is easy to do. People who write him off as a showman, clown or poseur on the basis of his (admittedly distinctive) sartorial taste, quips, mockney accent and fondness for pricking Establishment pomposities with a barb, are grossly underestimating his talent, intellect and capacity for sheer graft.

His rebellion against his starchy upbringing – a prodigy at the Yehudi Menuhin School, then three years in the hothouse atmosphere of the Juilliard School in New York – may have been long, noisy and sometimes hazy. But in all that time he never stopped practising the fiddle for hours every day.

Times Archive, 1941: Promenade Concerts

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As his mesmerising performance of Elgar’s Violin Concerto at his “come-back” Festival Hall concert in March reminded everyone, he’s still a world-class performer in mainstream classical repertoire. But grafted on to that core genius – or perhaps a different demonstration of it – has been his increasingly sophisticated excursions into jazz. It’s this breadth to his musicality that lifts him into a class of his own. If he were a sportsman he would have won Wimbledon twice, dabbled with international gymnastics and then turned himself into an Olympic-class swimmer.

The Proms audience will be getting a unique demonstration of that breadth. Because of Kennedy’s famous clash with a former Proms director – the late Sir John Drummond, who fatuously described him as the “Liberace of the violin” – and then his own self-imposed exile from British concert halls, he hasn’t appeared at the world’s biggest music festival for 21 years.

To make up for lost time he has a double engagement at the Albert Hall next Saturday. First he will play the Elgar in a conventional orchestral concert; then (as if that exhausting 50-minute journey were not enough) return with his jazz quintet for a 90-minute late-night set, including much of his own folk-rocky music. “I compose up in the hills, man,” he says. “I’ve found a little cabin in the mountains in Poland. It’s perfect. I play on the piano to get the structure, then track a violin over the top, then put it in front of the band to see how it goes.”

The band are Poles who have been knocking around with Kennedy for five years. I ask how he selected them. As with most things in his life, what seems on the surface to be random turns out to be carefully considered. “I met them all separately at jam sessions in the jazz club near where I live in Cracow,” he says. “I thought: that’s the drummer I want, that’s the bass player, and so on. They’ve all got their own projects.”

Can he speak Polish? “Enough to get a beer and some pity from both genders.”

So what attracted him to the Polish jazz scene? Indeed, what attracted him to Poland? “Same thing, really. The attitude of the musicians is what the people are like in the country as well. They are hard-working, but also know how to party. They’ve got intelligence, discipline and heart. It isn’t often you get all three together. And they aren’t clock-watchers. I found that with my orchestra [the Polish Chamber Orchestra, of which he’s artistic director] as well as with the band.”

Which, as Kennedy has famously made clear in the past, is not what he thinks about the British orchestral scene. He has been scathing about how little rehearsal he is granted with British orchestras.

“I can see where the problem comes from in Britain, and it’s understandable,” he says. “Musicians have to look at the clock here because they have to get to the next sesssion to pay their mortgage. But it does make life difficult when you don’t see the same faces in concert as in the rehearsal.”

Although Kennedy directs the Polish Chamber Orchestra from the violin, he doesn’t conduct it. The pointlessness, greed and general uselessness of conductors is another of his much-aired themes. “Actually, I envy conductors,” he says with a grin. “They don’t have to learn the music if they don’t want to – not really learn it, as you do when you play a concerto. If they put their arm in the wrong direction during a performance the orchestra probably won’t be put off. Whereas if you put your arm in the wrong direction when you are playing the violin, quite a lot of people will be put off.”

Conductorless or not, the EMI recordings that Kennedy has made with the Poles have created as much of a stir – though not quite so much outrage in sensitive circles – as his best-selling disc of Vivaldi’s Four Seasons, replete with sub-Hendrix sound effects. Coupled with his brilliant new recording of Beethoven’s Concerto, for instance, is a performance of Mozart’s Concerto No 4 that includes cadenzas incorporating jazz and world music. Composed by Kennedy, they are played on an electric violin with double-bass backing. That got the purists steaming.

“I can’t see that Mozart would have minded,” he grins. “He wasn’t exactly averse to the technical developments of his own day. He embraced the piano when he could have carried on playing the harpsichord. He would probably have loved to bomb out the ears of some aristocrat with something electric.”

Does this mean that Kennedy’s long-standing antipathy to Mozart is now officially at an end? “I had a bad experience a long time ago, when I improvised a cadenza in a Mozart concerto, got in a terrible mess, ending up sounding like Debussy, and then – when the orchestra came in – found I was in the wrong key. I left Mozart alone for 20 years after that. But that was also the time when the horrible authenticity movement was around, and I didn’t relate to that.”

In its way Kennedy’s recording of two rarely played Polish violin concertos, by Emil Mlynarski and Mieczyslaw Karlowicz (don’t pretend you’ve heard of them), is equally revealing. It’s not that the music is particularly startling, though both concertos are ripe, late-Romantic pieces full of fervour, tunes and scintillating figuration. It’s more what they say about Kennedy’s unquenchable musical curiosity. Six years ago, after he played the Elgar concerto in Warsaw, an audience member handed him an old recording of the Mlynarski. Many star fiddlers would have feigned delight and promptly tossed the disc away. Kennedy played it, loved it, resolved to champion the work afresh, and has kept his pledge.

Has he got any more unknown Polish concertos in the pipeline? “I’m on the lookout, man! I love playing Romantic music, something with a bit of meat in the harmonies and some expansive architecture in its structure. Something to get your teeth into. Know what I mean?”

Kennedy is at the BBC Proms (0845 4015040) on July 19 2008. A Very Nice Album by the Nigel Kennedy Quintet is out on EMI. The quintet tours in the autumn

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