Still was born in London on 10 June 1910 into a family with a strong interest in music. He was educated at Eton College (1923–29) and Trinity College, Oxford, where he graduated in history and French, and then in music. He had a younger brother who died aged 16 and a sister who emigrated to Australia.
At school and at university Still developed a lifelong interest in racquet sports, including real tennis, in which he won a university sporting blue. Both his father and grandfather were solicitors in a long-established London firm, and he had been intended for the law. He studied music at Oxford under Ernest Walker, Sir Hugh Allen and others (ancestor Peter Still had acted for George III), and then spent two years at the Royal College of Music under C. H. Kitson, Basil Alchin and Gordon Jacob. He also studied under Wilfred Dunwell at Trinity College of Music (modern harmony and counterpoint) and later in life under Hans Keller.
Still returned after Oxford to teach music at Eton, moving on in 1938 to become conductor and arranger of the Ballet Trois Arts, a travelling company. Having refused a commission, he spent the Second World War first manning a searchlight in the Cotswolds and then with the Royal Artillery travelling orchestra, which he conducted. He married in 1944 and had four daughters.
After the war, the couple moved to Ampfield, Hampshire and in 1949 to Bucklebury, Berkshire. He then devoted himself to composition, although he had considered becoming a Freudian lay psychoanalyst. This interest led him to form the London Imago Society in 1956, along with a friend, Adrian Stokes. An article by Still on the psychology of Gustav Mahler was published by The American Imago Society. He also sat on a selection board for Berkshire Education Authority and advised prospective students over a period of 15 years.
Still died of a heart attack on 13 January 1971, having just been elected to the Executive Committee of the Composer's Guild.
Still had already written some songs and a since-lost light opera for the Windsor Operatic Society, for which he was the conductor while still teaching at Eton. His compositions came to include many other songs, four symphonies, a piano concerto, a violin concerto, instrumental and chamber works, orchestral works, motets and an opera (Oedipus, to a libretto by Adrian Stokes).
Still's Third Symphony was submitted to the University of Oxford in 1963, after being championed by Sir Eugene Goossens, the conductor. This earned him an Oxford doctorate in music. Some of his chamber works were recorded by Argo Records. An archive is held at the Jerwood Library of the Performing Arts in Greenwich. His work remained predominantly tonal, with strong use of dissonance. A number of earlier recordings from the 1960s and 1970s were revived for his centenary in 2010. The "fearsomely difficult" violin concerto was revived in 2013 in Ealing, London. His work made its CD debut in 2010, with a selection of chamber pieces originally recorded in the 1950s. His third and fourth symphonies have also been reissued in CD form.
Much of his time in later life was spent giving free advice and lessons to students. His friends included Deryck Cooke, Anthony Scott, Adrian Stokes, the painter and critic, the harpsichordist Michael Thomas, Sir Eugene Goossens, and Myer Fredman, the conductor. In an obituary, The Musical Times wrote of him as "a song writer of genuine lyrical impulse [who] set words by Byron, Keats and Shelley; he was also a symphonist, in a conservative vein."