Best known for her work with the band Henry Cow, she was also a member of Comus, National Health, News from Babel and David Thomas and the Pedestrians.

She collaborated with a number of musicians, including Chris Cutler and Sally Potter, and co-founded the Feminist Improvising Group.

She added oboe and flute to her instrument repertoire, and started doing session work for other musicians, including Mike Oldfield on his album Hergest Ridge (1974).

While working on a theatre project, Cooper encountered Henry Cow, an avant-rock group that would later launch her musical career on the world stage.

In late 1973, Henry Cow asked Cooper to join them as a replacement for Geoff Leigh (tenor sax and flute) who had recently left.

In 1977, Cooper became one of Henry Cow's principal composers and contributed a number of compositions to their repertoire, including half of their final album, Western Culture (1978).

In 1980 she recorded her first solo album Rags, a song-cycle about sweatshops in Victorian England, with Chris Cutler, Fred Frith and Georgie Born (all from Henry Cow) and Phil Minton and Sally Potter.

During the 1980s, she toured the United States with David Thomas and played in various bands in England led by jazz composer Mike Westbrook.

In 1983 Cooper collaborated with Chris Cutler and formed the English avant-rock group News from Babel, composing all the music for their two albums, Work Resumed on the Tower (1984) and Letters Home (1986).

Sahara Dust was released on CD in 1993 with the voice of Phil Minton, and reflected on the 1990–91 Gulf War and its impact on the world at large.

[9] In a review of the Barbican concert on 21 November, Dom Lawson called it "a fitting salute to Cooper's life", adding "what tonight's experience never becomes is self‑indulgent: there's a sharpness to the intricate arrangements as very obvious waves of passion and commitment from everyone on stage flow and spread across the auditorium.