Stevens was born in Brentford, the son of a tap dancer. He listened to jazz as a child but was more interested in drawing and painting, through which he expressed himself throughout his life. He studied at the Ealing Art College and then started work in a design studio but left at 19 to join the Royal Air Force. He studied the drums at the Royal Air Force School of Music in Uxbridge, and while there met Trevor Watts and Paul Rutherford, two musicians who became close collaborators.
In the mid-1960s Stevens began to play in London jazz groups with Tubby Hayes and Ronnie Scott, and in 1965 he led a septet. He moved away from mainstream jazz when he heard free jazz from the U.S. by musicians like Ornette Coleman and Albert Ayler. In 1966, he formed the Spontaneous Music Ensemble (SME) with Watts and Rutherford. The band moved into the Little Theatre Club at Garrick Yard, St. Martin's Lane, London. In 1967 their first album, Challenge, was released. Stevens then became interested in the music of Anton Webern, and the SME began to play quiet music. Stevens also became interested in non-Western music.
In 1967, Evan Parker joined the SME and became one of the longest-standing members. He later summed up Stevens' approach to improvising in two basic maxims: if you can't hear another musician, then you're too loud; and there is no point in group improvisation if what you are playing doesn't relate to what other members of the group are playing.
Stevens also devised a number of basic starting points for improvisation. These were not "compositions" as such, but rather a means of getting improvisational activity started, which could then go off in any direction. One of these was the so-called "Click Piece" which essentially asked for each player to repeatedly play a note as short as possible.
Stevens played alongside a large number of prominent free improvisors in the SME, including Derek Bailey, Peter Kowald, Julie Tippetts and Robert Calvert, but from the mid-1970s, the make-up of the SME began to settle down to a regular group of Stevens, Nigel Coombes on violin, and Roger Smith on guitar. During the mid-1970s Stevens played regularly with guitarist and songwriter John Martyn as part of a trio that included bassist Danny Thompson. This line up can be heard on Martyn's 1976 recording Live at Leeds.
From 1983 Stevens was involved with Community Music, an organisation through which he took his form of music making to youth clubs, mental health institutions and other unusual places. Notes taken during these sessions were later turned into a book for the Open University called Search and Reflect (1985). In the late 70s and early 80s John was a regular performer at the Bracknell Jazz Festival.
Stevensran or helped to organise groups that were more jazz or jazz-rock based, such as Splinters, the John Stevens Dance Orchestra, Away, Freebop, Folkus, Fast Colour, PRS, and the John Stevens Quintet and Quartet. He contributed to Trevor Watts's group Amalgam, Frode Gjerstad's Detail, and collaborated with Bobby Bradford on several occasions.
SME played for its last time in 1994, when it included John Butcher. Stevens died later that year.Somewhere in Between (Vertigo, 1976)
Touching On (Vinyl, 1977), with Allan Holdsworth, Jeff Young, Ron Mathewson
No Fear (Spotlite, 1978), with Trevor Watts, Barry Guy
Vols. 1 & 2 (Nessa, 1980–81) with Bobby Bradford
Radebe – They Shoot to Kill (Affinity, 1987) with Dudu Pukwana
With the Spontaneous Music EnsembleQuintessence (Emanem, 1974 )