When I first went to Amaryllis in 1967, aged 14, I had just decided that I wanted to be a cellist, whereas for the previous six years I had not been serious about music. I would never practise, and my other teachers had despaired of me, saying "He's gifted but lazy".
I was at Latymer Upper School, in Hammersmith, west London, where the extra-curricular emphasis was very much on drama. My best friend was Mel Smith of Smith and Jones fame. We sat next to each other in class and acted together. I was much more interested in becoming an actor than a musician.
But at 14, my mother, also a cellist, took me to hear the Brahms double cello concerto played by Zara Nelsova and Ida Haendel. They gave fantastically charismatic performances which changed my life. I thought:
"This is what I have to do."
My late father, a fine pianist, was playing recitals with Amaryllis at that time and suggested I become her pupil. She wasn't teaching very much, because of her heavy concert schedule, but she agreed.
On Saturdays I would take my cello on the bus from our home in north Kensington to her house in south Kensington. The other passengers would see the case and say things like "How do you fit that under your chin?" Amaryllis had an extraordinary background. Her father was the painter, Augustus John, but she only found that out when she was 20, having been brought up by her mother. Her half-brother was the author Ian Fleming. She had trained with Pierre Fournier and with the great Madame Suggia.
Amaryllis was famously beautiful, with auburn hair and fine features. Her slender build meant it was never easy, physically, for her to play the cello, and I think that's one reason she was such a good teacher.
Her teaching was very much an extension of her own practice, and I've inherited a lot of my methods from her. I often give my students pieces I'm working on, as she did with me.
At the time, she was thinking carefully about her own bowing technique and would take me through many difficult exercises. I quickly realised I couldn't play demanding pieces properly unless I buckled down and did the technical work. She was dead strict, but she also had - and has - a wonderful sense of humour.
She liked to drink whisky and smoke, and when she demonstrated - taking hold of my arms, and saying "You see, dear, you do it like this' - there'd be this wonderful smell of whisky and cigarettes on her breath, the memory of which will always stay with me.
The first time I heard the Elgar concerto was listening to Amar-yllis at the Swiss Cottage Odeon, north London. Hearing my teacher play that work made a huge impression. Everything she talked about in the lessons came together in performance.
The other extraordinary thing was that, while many music teachers are possessive of their good students, she was the reverse. When I was 16 and the question arose of whether I should leave school and devote myself full time to music, she thought it would be a brilliant idea for me to study with Ama-deo Baldovino in Italy. She said it would be a real eye opener for me - and she was absolutely right.
After Italy, I went to the Royal Academy and then to California, to study with Gregor Piati-gorsky, the great Russian cellist. He was another huge influence and, because I was 19 by then, he and I could talk about things - books, sculpture, chess, growing old - that I was too young to discuss with Amaryllis. She and I are still close friends, and now chat about everything.
As a player she taught me to be open to everything in music. She played everything from baroque to new works, and so do I. I've certainly followed her example as a teacher. I'm happy to pass my students on to other people if I think it's the right thing to do. I hope I also have something of her generosity of spirit: trying always to think not of what you can get out of your pupils, but what you can give to them.
Raphael Wallfisch, 44, cellist andprofessor of cello at the Guildhall School of Music and Drama, London, has given concerts and master classes all over the world. He has recorded more than 30 CDs, including the complete Vivaldi cello concertos. Tonight (March 6) he performs in Manchester at New Broadcasting House; March 21 with the BBC National Orchestra of Wales at North Wales Theatre, Llandudno; March 26 with the London Mozart Players at Anvil, Basingstoke. He was talking to Daniel Rosenthal