Delia Ann Derbyshire was born in Coventry in 1937, the daughter of Edward (a sheet metal worker in a car factory) and Mary Amelia Derbyshire. Only a few years later, Coventry became a major target for German bombing raids, and Derbyshire later realised that her love for abstract sounds came in part from the air-raid and 'all clear' sirens she heard as a very young child. During the worst of the blitz, she was evacuated to Preston in Lancashire, where her parents came from; she subsequently recalled the clatter of the mill-workers' clogs on cobbles as another sound that influenced her.
She attended Barr's Hill School for Girls in Coventry, and her academic career at school is well-documented in this collection. She did not study music in any depth at school, although she excelled at the piano in her spare time, taking part in competitions and reaching performer level (music is described as her "favourite hobby" in one of her school exercise books). She obtained a place at Girton College, Cambridge, to read mathematics, and although she later switched to a music degree, her fascination for maths and its relationship with music shaped much of her work as a composer.
After university, she hoped to pursue her interest in sound, music and acoustics, but on applying for a job at Decca Records she was told that they did not employ women in the recording studio. However, in 1962 she managed to obtain a post as trainee studio manager at the BBC, and was soon seconded to work at the BBC's Radiophonic Workshop, which had been set up to provide theme and incidental music and sound for BBC radio and television programmes. The following year, she produced her electronic 'realisation' of Ron Grainer's theme tune for the hugely popular BBC series Doctor Who - which is still one of the most famous and instantly recognizable television themes.
Derbyshire continued to produce innovative work in what was initially a largely analogue environment, involving labour-intensive tape splicing and speed adjustment, as well as making use of oscillators and 'found' sounds (she famously used a tatty lampshade which she thought provided a beautiful ringing tone). She moved on to work with synthesizers, although she disliked the increasing trend of using synthesizers to mimic traditional instrumental sounds. The Workshop's TV output soon overtook its work for radio, and Derbyshire provided music for drama, science, arts and educational programmes, establishing herself as one of the pioneering figures in British electronic music.
Outside of the Radiophonic Workshop, she worked on various projects, creating music for theatre, film, festivals and 'happenings'. She collaborated with numerous well-known figures, including the German composer Karlheinz Stockhausen and Peter Maxwell Davies. She worked with Peter Zinovieff (founder of the EMS synthesizer company) to establish Unit Delta Plus - an organisation to create and promote electronic music; as part of this initiative she also worked with Paul McCartney and George Harrison on a piece called The carnival of light performed at the Chalk Farm Roundhouse in 1966, and created a film soundtrack for Yoko Ono. She also worked with or influenced other musicians and bands such as Brian Jones and the Rolling Stones, Pink Floyd and - perhaps surprisingly - Anthony Newley.
Derbyshire decided to leave the BBC in 1973; by this time she felt disillusioned with the corporation's increasing antipathy to the kind of unusual, abstract music she wished to make, and was unwilling to compromise her integrity. She moved to Cumbria, working in a range of jobs; for a time she was a French-bilingual radio operator for British Gas on a major pipeline laying project. She subsequently worked with the abstract artist Li Yuan Chia - one of the most important Chinese artists of the twentieth century - and went to live at his LYC Museum near Hadrian's Wall. It was an environment in which everyone was encouraged to participate in a wide range of arts, and Derbyshire worked alongside Li Yuan-chia in running the gallery and printing press, exhibiting the work of artists and poets, and organising events and readings.
After a long time away, Derbyshire returned to music and composition in the late 1990s; this period saw renewed interest in her work, and many younger musicians making electronic dance and ambient music (such as Aphex Twin and The Chemical Brothers) cited Derbyshire as an important influence. She collaborated with Sonic Boom (Peter Kember, formerly of Spacemen 3) on two albums released under the name Experimental Audio Research: Vibrations (2000) and Continuum (2001).
Derbyshire married David Hunter in 1974; the couple subsequently separated and from 1980 (around which time she moved to Northampton) her partner was Clive Blackburn. She died on 3 July 2001.