Hair-raising, visionary and impetuous, the Russian conductor Valery Gergiev whips you into a fresh understanding of any music he tackles, whether you like it or not.

His Mahler Symphonies cycle with the London Symphony Orchestra at the Barbican — which he is now halfway through — has startled, mesmerised and maddened. Some can't stand it. Others have started out sceptical, calling him a Mahler novice — all dark Russian angst, no airy Viennese irony — then seen the light and turned evangelical.

If you've missed the fireworks in the concert hall, you can now listen at home for a mere £8. Next Monday LSO Live, the orchestra's top-selling budget label, releases its inaugural CD with their new principal conductor.

It's a white-knuckled account of Mahler's tragic Sixth Symphony, famous for its bizarre, shunting cowbells and shattering hammer blows. In Gergiev's excitable, baton-less hands, the pace is fast, the aural colours glint and flash, the orchestra sounds edgy, taut and exhilarating.

The complete Gergiev/Mahler cycle, which culminates in the mammoth Symphony of a Thousand (No 8) at St Paul's Cathedral in June, will be released over the coming year. This is a coup for LSO Live.

Why? The completist-obsessed CD world is awash with Mahler. My Mahler-addict colleague, Norman Lebrecht, has a dozen box sets, each running to 15 hours each. LSO Live itself launched in 2002 with a fine recording of the same Sixth Symphony by Mariss Jansons, Apollonian to Gergiev's burnished, Dionysian approach. Do we need more?

“Look,” Gergiev, 54, says firmly, fingering a Mahler score as he prepares for an afternoon rehearsal at LSO St Luke's. “I am principal conductor of this astounding orchestra. We are on this symbolic journey together. The musicians have played this music many times before. I have conducted these symphonies many times before. But together we are saying something new.”

Inevitably, given his workaholic reputation, this charismatic figure is preceded by an elaborate mythology. It has always been part of his charm. Since he first sprang onto the London scene more than two decades ago, he has been the darling of audiences and orchestras, every concert an event, an excitement, with a whiff of danger in the air.

But when his LSO appointment was announced two years ago, the carping began in earnest: that he crams too much into his jet-setting life, is always late, doesn't rehearse and, crazy-haired and stubble-chinned, always looks a mess.

That last prejudice, at least, is immediately punctured. We meet in a small green-room at LSO St Luke's. Gergiev's first gesture on entering is to find a mirror and comb, pulling it across his head vigorously. Important to have neat hair before an interview, I jest. Yes, he says, taking me literally.

His English is not fluent and his Russian friends say that in the process of getting the words right, his sharp humour doesn't always show through. He then takes off his coat and jacket and, with immense care, hangs them on hangers. Shoes are polished, trouser-creases sharp.

Yes, he's late but it's a calculated lateness: keeping a journalist waiting is allowable if it means a chance to grab a few minutes on the phone with an agent in New York or an organiser of his White Nights Festival in St Petersburg, or one of his three young children (he has two sons and a daughter, all under 10) or his young wife, Natalia, or his elderly mother at home in Moscow.

His commitments span every corner of the globe, which means an exhausting schedule of perpetual travel: in addition to the LSO, he is artistic and general director of the Mariinsky Theatre, St Petersburg, principal guest conductor of the Metropolitan Orchestra and principal conductor of the Rotterdam Philharmonic.

But whatever the excuses for his seat-of-the-pants timekeeping, he inevitably causes nail-biting when he doesn't show up. “I am not normally late,” he defends himself. “When I am, it's often because of travel. More than ever after 9/11, you cannot control it if you are kept waiting. They don't care who you are. When, however, I am performing well-known works with an orchestra, it is not the number of hours we spend but the concentration.”

Musicians, not by any means the biggest fans of conductors, don't seem bothered. They are unanimous in admiration for him. Gergiev, they say, can command precisely the sound he wants with the merest flick of a finger. As a trumpeter in the New York Philharmonic Orchestra comments: “It is not the extraordinary things Gergiev does. It's the extraordinary things he gets us to do.”

Last month Gergiev was in London with the notoriously tricky, self-governing Vienna Philharmonic, which has its own playing style and tradition. It has never had a chief conductor and unceremoniously dumps anyone who is less than superlative.

“I cannot teach great professionals such as those in the Vienna Philharmonic or the LSO to play the notes,” Gergiev insists. “They know them. And it would be very arrogant for me as a conductor to think they will remember every word I tell them in a rehearsal. So what we do is certain bits, with others left out. It's all about focus. Concentration. That way we keep a performance fresh. There are two kinds of conductor — those who surprise in a concert and those who prefer not to. Neither is better, just different.”

Gergiev is one part of the triumvirate of world-class conductors — Barenboim and Simon Rattle being the other two — who not only make extraordinary music in the concert hall but force action outside it.

Single-handedly, with heart and emotion and indefatigable energy, he revitalised musical life in the turmoil of post-Soviet Russia. After the Beslan school massacre it was Gergiev, whose family is from the region, who caught the public imagination when he went on television and appealed for calm, as well as giving fundraising concerts, tears streaming down his face.

In Russia he gives 20 performances a year unpaid with the Mariinsky, so that young people in schools and universities can attend free concerts. “Can you imagine the orchestra of the Royal Opera or the Bastille or the Met doing that? Musicians unpaid? Playing perhaps an entire opera in concert? We do many things free, for thousands of people, and we don't shout about it. We can't expect families on low pay to spend a 10th of their income to go to an opera.”

The son of an army officer, Gergiev grew up in rural, mountainous Ossetia, studying at the local music school (now named after him) before going to St Petersburg. After the death of his father, the 14-year-old was encouraged by his mother and two sisters. The family remain close.

“My mother is living with us,” Gergiev says, smiling for the first time. “She is 83. She can teach my children what she learned from trying to bring me up. I was a normal boy, football crazy, not thinking about music all the time. It pleases me that she has this role now. She is the most important person in their lives.” His wife may well have other views on the matter.

Still immersed in the musical politics of Russia, Gergiev counts Putin as a friend and made a point of voting for Medvedev at the Russian Consulate in New York. He quickly condemns any cynicism about the recent elections.

“Listen to me. Our country was shaken from top to bottom for 70 years. You didn't experience the First or Second World War as we did. Your country didn't suffer poverty and oppression as we did. Putin brought us stability. There are a few people who don't like him, like [Boris Abramovich] Berezovsky. But there are people who don't much like Berezovsky, too.”

He pauses to refine this point. “Seventy per cent of people voted for Medvedev. They cannot all be such idiots?”

He's about to say more. But the call comes for the rehearsal to start. Obediently, Gergiev picks up his Mahler score, combs his hair again, straightens his shirt and goes upstairs. He is bang on time.

www.lso.co.uk.