King was a noted champion of obscure clarinet works of the 18th and 19th centuries, particularly those of Bernhard Crusell, Franz Krommer, Louis Spohr, Carl Stamitz and Carl Maria von Weber. An accomplished pianist, she won a piano scholarship to study at the Royal Conservatory of Music, where she was a pupil of Arthur Alexander and clarinetist Frederick Thurston. "In those days it helped if you played two instruments, however poorly," The Daily Telegraph quoted her once saying. At the piano King often accompanied her clarinetist peers, including Gervase de Peyer and Colin Davis.
In 1953, King married Thurston, only to see him pass away at the end of that year. She took after much of his playing style and musicianship.
"He taught me that it was possible to play more beautifully and more convincingly than I had ever dreamed of, and that it must take incredible courage and idealism," she was quoted as saying in The Daily Telegraph. They did not have children, nor did she remarry.
Embarking on a career as pianist and clarinetist, she gradually focused more on the latter instrument, playing on a number of occasions for Benjamin Britten at the Aldeburgh Festival. She founded in 1953 the Portia Wind Ensemble, an all-female double wind quintet with which she played for 13 years. The group gave many important premieres and garnered acclaim for bold programming.
King was disappointed by the domination of males in orchestras and later remarked after a performance by the Dresden Staatskapelle led by Kurt Masur, "I scanned the orchestra eagerly, but there was not a skirt to be seen."
Between 1955 and 1984, she played with the London Mozart Players, succeeding de Peyer as its principal clarinetist, and later taught at the Royal Conservatory from 1961 to 1987. She was appointed to the Guildhall School of Music in 1988.
In 2001, she was named a Dame Commander of the Order of the British Empire, the first wind player to receive the female equivalent of a knighthood.
King has made many recordings of both solo and chamber music works, sometimes performing in dual roles; she recorded a Brahms clarinet sonata and a Mendelssohn concert piece for clarinet, basset horn and piano, playing all the instruments. Her recording of the clarinet concertos by Charles Villiers Stanford and Gerald Finzi was the first title ever released by Hyperion Records.
Her focus fell back onto the piano during the 1990s, and in 2001 she played the piano part of John Ireland's Fantasy Sonata for clarinet and piano (which she had already recorded playing the clarinet part) in a centenary concert in honor of her late husband.
Compositions dedicated to King include Howard Blake's Concerto, Benjamin Frankel's Quintet, Gordon Jacob's Mini Concerto and Maconchy's Fantasia.
Committed to young artists, King was a judge in last year's BBC Young Musician competition. Her former students include Michael Collins, Richard Horsford, Colin Bradbury and David Campbell.