They called him “Slava”, which is what the peasant chorus in a Russian opera sing, repeatedly, when someone like the Tsar turns up. The word means “glory”. And it captured everything you would want to say about the big, bearhugging, hundred-watt personality of Mstislav Rostropovich, who was not only one of the great musicians of the 20th century but in many ways one of the great human beings.

When he died last year it triggered memories of him as a cellist of giant emotional dimension; as a conductor with an inscrutable beat that orchestras somehow learnt to read and love; and as a world figure with the clout to unsettle or endorse political regimes. There he was defending Solzhenitsyn, denouncing Leonid Brezhnev, or embracing Boris Yeltsin in the firing line of hostile tanks.

But for the star cellists - Mischa Maisky, Natalia Gutman, Moray Welsh and more - who will file onstage at Cadogan Hall on Sunday for a belated tribute concert, there's another memory. They were all his pupils: graduates of the legendary classes that Rostropovich held in Soviet Russia in the 1960s. They talk about the experience as though it happened yesterday, using images such as “torrent”, “ice-break” and “hurricane” to describe the impact on their lives.

For 25 years, until he left Russia in 1974, he taught in both the Moscow and Leningrad conservatories, with a particularly famous class in Moscow, Class 19, that was the hot ticket of its day. At a time when speech was guarded, Rostropovich's Class 19 was provocative and maverick. His students called him “Sunshine” and accepted his impetuous demands to learn a concerto in two days or come back and play the Bach Cello Suites from memory in a week. No excuses.

“Let's be honest, we were quite afraid of him,” Karine Georgian, another of his students, says. “We hung on his every word, and it wasn't always kind. I never forget him saying to me when I played Brahms in his class: ‘You haven't cried enough tears in your life to play this music'. Actually he was right, I hadn't. But I learnt.”

For Maisky, the price of attending Class 19 turned out to be more than just tears. It was a year and a half in a labour camp, brought about by his habit of taping everything that Rostropovich said. “The class was so incredible, and he worked at such speed, it was impossible to absorb; so for years I took along an old second-hand tape recorder, and eventually I needed to replace it. But these things were hard to get: only from the special shop with special certificates.” Getting the certificates involved a black-market currency deal for which he was arrested and put on trial. “The whole thing was a set-up. They'd been watching me because my sister had emigrated to Israel and they expected me to do the same. It was their revenge. But one-and-a-half years was lucky. I could have got eight.”

Whether Rostropovich helped to get the sentence reduced isn't clear. Maisky thinks not, because his influence had collapsed over his support for Solzhenitsyn. “Until then he had power, he could ring up Brezhnev. After Solzhenitsyn his power was lost, so there was nothing he could do for me. Except in personal terms. In that sense he was like a father. He sent money, he maintained my spirit ... so many things.”

Some students, though, were actively encouraged to court danger. Moray Welsh, until recently the LSO's principal cellist, attended Class 19 from 1969 to 1971 and remembers being dragged, reluctantly, into an abortive plan for Solzhenitsyn to defect to England.

“There I was, a youngster from Britain keeping my head down as I'd been advised to, and one day Rostropovich beckons me over and asks if I'll take a message to the British Embassy. It was the time when Solzhenitsyn had just been awarded his Nobel prize, to the annoyance of the Kremlin, and he was being sheltered in Slava's dacha outside Moscow. The plan was for him to go to Stockholm, get the prize, and then defect to London. And I was to be message-runner.

“In the end he didn't get as far as Stockholm because the Soviets said they wouldn't allow him back if he went, and that took the ground from under his feet. Defection would have served no purpose. But I did what Slava asked, although I felt uncomfortable about it and worried if the whole thing was a set-up job to push me out of the country.

“I idolised Rostropovich like everyone else, but you never knew what was going on, and there were liaisons between people you'd never expect. Rostropovich had an assistant/right-hand-man who was unquestionably KGB. And though Rostropovich made fun of him behind his back, they had a close, mutually dependent relationship that was hard to read.

“Another odd relationship was with Ekaterina Furtseva, the fierce and powerful minister of culture. Theoretically they were enemies, and she caused him many problems. But he told me that on one occasion she approached him, tears running down her face, and said: ‘Slava, why are you doing this to me?' And telling the story, he added: ‘You know, I really admired that woman. She was stuck in the system too. We were all victims.' It was extraordinary to hear him say that.”

Welsh has been a driving force behind Sunday's concert, which also involves members of the LSO and other musicians with Rostropovich connections. It's been organised partly to raise money for the childcare foundation that Rostropovich and his wife created, but also because, as Welsh says, “there's been nothing in London to commemorate him since he died; it's time there was”.

The event is running under the auspices of the London Cello Society: a fan club for the instrument which is just the kind of thing Rostropovich loved and fostered. In a short film likely to appear on the roster he commends the “enormous, brilliant friendship, very rare” of cello gatherings. He also gives an explanation for their friendliness: “We carry heavy instruments and suffer so much on planes and trains. This makes us sympathetic people.”

Slava! - A Tribute to Rostropovich is

at Cadogan Hall, SW1 (020-7730 4500)

on Sunday

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