She made electronic music in the 60s when women just didn't DO that sort of thing (Decca Records refused to hire her,) and worked for the BBC's legendary Radiophonic Workshop. She stopped making music in the mid 70s because she thought that modern equipment made it too easy. However, she had been working with some younger electronic artists prior to her death in 2001.
She is responsible for the sound of the classic Doctor Who theme (although it was written by someone else, when it was played back for him by Delia, he asked "did I write that?")
http://www.delia-derbyshire.org has the full scoop on her life and works as well as some mp3s. Check it out.