Oliver is a former member of the band Rip Rig + Panic; one of their notable television appearances came when they performed in an episode of the cult comedy show The Young Ones. She used to co-host the Channel 4 television show Baadasss TV alongside Ice-T and frequently appears on the BBC World Service and the BBC's annual coverage of Glastonbury Festival.
Other music projects
After 1983, Oliver became involved in Kalimba – an African inspired band. In 1990 she joined forces with her brother, forming the Mighty Hog.
In April 2007, she started presenting a six-part cookery show Neneh and Andi Dish it Up with her close friend Neneh Cherry for BBC2.