Levy's father was a member of the African National Congress, an academic, a historian. The family emigrated to Wembley Park, in 1968. Her parents divorced in 1974.
Levy trained at Dartington College of Arts, leaving in 1981 to write a number of plays, including Pax, Heresies for the Royal Shakespeare Company, and others which are published in Levy: Plays 1 (Methuen)
She was director and writer for Manact Theatre Company, Cardiff.
Deborah wrote and published her first novel Beautiful Mutants, in 1986.
She has always written across a number of art forms (see Bookworks and Collaborations with visual artists) and was Fellow Commoner in Creative Arts at Trinity College, Cambridge from 1989-1991.