That people are unique is a truism; in Fleming's case it was an understatement. Born she never knew where (Switzerland, perhaps) on 10 December 1925 (probably), she had an upbringing more extraordinary than most. Raised as the adopted daughter of Eve Fleming, a beautiful, strong-willed war widow, her childhood was blighted by loneliness and uncertainty. She had few friends, disliked her adoptive mother, never felt she belonged in the Fleming family - although she got on with Eve's four sons, who included the writers Peter and Ian - and particularly resented the lack of any true parents.
Had Eve been more truthful, much heartache could have been avoided: Amaryllis was, in fact, her natural daughter, the result of an affair with the artist Augustus John; but, for reasons of her own, Eve maintained the pretence and elaborated upon it - Amaryllis's mother was dead and her father untraceable, she said with melancholy satisfaction. As a child Amaryllis was conscious of being a second-class citizen, dressed up as a party-piece for Eve's guests before being sent to play in the garden.
Eve's subterfuge became increasingly transparent. Not only had Amaryllis inherited John's red hair but she looked astonishingly like her mother. When Eve said that people who lived together grow to look like each other, Amaryllis was the only one who believed it. In 1949, however, when she was 24, the rumours reached such a pitch that Amaryllis confronted her parents.
Eve denied everything, Augustus on the other hand hemmed and hawed. He shouted that nobody knew who she was, banged his fist on the table, said that she was born in a ditch, and then finally relented. "So you're my little girl, are you? Don't tell your mother."
Amaryllis found herself in possession of 13 half-brothers and sisters, John and Fleming, whose occupations ranged from author, explorer, spy and banker to boxer, actress, painter and admiral. She also found a home at Fryern Court, John's house in Hampshire, where she was welcomed not only by Augustus but also by Dodo, the mother of four of his children, with whom she reached an immediate rapport.
From her bizarre upbringing, which might have squashed a lesser person, Amaryllis acquired a sense of rebellion and independence. From John she inherited a temper, an inability to remember dates, and a strong libido. From Eve she received a lot of moles, great beauty and, importantly, musical talent. Trained on the piano at the age of four, she graduated to the cello when she was nine and by her late teens was a prize-winning pupil at the Royal College of Music.
She studied under Guilhermina Suggia, whom she hated, Pablo Casals, whom she admired, and Pierre Fournier, with whom she had an affair. Like so much that she did, this last did not endear her to her mother. Peter Fleming was ordered to have a word with Fournier in the Hyde Park Hotel. It was a severe word. "I cannot see you again," Fournier told Amaryllis afterwards, "I will never know if one of your brothers is hiding under the bed with a pistol."
He retired to Paris and did not emerge for several weeks. His wife, Lyda, was a model of Gallic understanding. Some years later, when the affair had ended, Fleming was invited to dinner chez Fournier and was seated between Pierre and his 19-year-old son. Lyda suddenly hoisted the tablecloth and peered underneath. "Amaryllis!" she cried, "This is too much! Both my husband and son are playing with your feet."
Following her first Prom in 1953, in which she played Elgar's Cello Concerto conducted by John Barbirolli, Fleming became the leading cellist in post- war Europe. She took numerous prizes and in 1955, with Lamar Crowson, won the cello-piano section of the Munich International Competition. While shuttling between venues she also played in guitar trios with Julian Bream and John Williams.
She would have retained her supremacy were it not for the advent of Jacqueline du Pre in the Sixties. Unable to compete with the sheer power of du Pre's playing, she sought new avenues. She had always been an innovator, famously, in the Fifties, she spent two months with Ricardo Nani in Bologna, during which time she practised naked in front of a mirror to analyse her posture. Now, in the Sixties, she analysed her instrument.
Rejecting for a while the standard four-string cello, she found and resurrected an original five-string Armati. Music for five strings existed but nobody knew how it should be played. Fleming rediscovered both the cello and the technique, thereby inaugurating the modern trend for Baroque. Ground- breakingly, she became the first person this century to play Bach's Sixth suite in the manner its composer had intended.
Fleming was, in her own words, "a musician's musician". She used the term as an excuse for not having made any recordings, but it was accurate nonetheless. From the Sixties her career was dominated by recitals and chamber music, for which she received critical acclaim but which brought none of the glamour of a solo career. She was also an inspiring and individual teacher, eventually becoming - somewhat to her rebellious dismay - a professor at the Royal College of Music.
Her final, and most appreciated performances, were with Bernard Roberts and Manoug Parikian, a trio which lasted from 1976 until 1983 when Roberts dropped out and was replaced by Hamish Milne. They were, according to one review, "like some rare and distinguished delicacy from the highest class of delicatessen". Parikian died in 1987 and with him the trio. From that date she continued to teach but made only the occasional performance. In 1993 her cello-playing days were ended by a stroke. Deprived of her spiritual mainstay - Bach's suites - she turned to Tibetan Buddhism, which provided her with invaluable support during her final illness.
Shortly before her stroke I was privileged to be Am's biographer. It was a hilarious process from which I gained much. Approaching her home in South Kensington the whiff of difference was palpable: cobbles on the street, plants bulging out of barrels, a note for the milkman in an empty wine-bottle and - if you were lucky - one of Bach's suites wafting from a downstairs window; if you were less lucky, a window opening above and the words, "Oh I thought you were the fish man." Then, as the window closed, a giggle. As to what or whom you might find within . . . suffice to say, I once discovered a Bhutanese princess discussing which colours were most auspicious in the Cheltenham Gold Cup.
From all the extraordinariness of Amaryllis Fleming's life it is oddly, an event of utter mundanity which remains uppermost. Driving one night with Am to see her judge a competition at the Royal College of Music, I wondered why only her sidelights were working. She said the switch was broken and made a lot of derogatory remarks about the mechanic. "He had the cheek to ask me if I was pressing the button properly," she finished. "I told him, `What kind of a fool do you think I am?' " As we crept dangerously up Exhibition Road I leant over and pressed the switch a notch further. The headlights came on. There was a moment of silence and then she began to laugh. I forget who took part in the competition, what instruments they played or who won. But I do remember that laugh.
Everyone who knew Am Fleming will remember her laugh. It was unlike any other: smoky, wild, infectious, full of the glee of life. We will all miss it.
Amaryllis Fleming, cellist: born 10 December 1925; died London 27 July 1999.