Stephenson worked as an actress with the Royal Shakespeare Company and in bit parts in television.
She has subsequently had parts in Rumpole's Return, Sapphire & Steel, The Gentle Touch, The Adventures of Sherlock Holmes, Boon, Paradise Postponed and Big Deal.
Her original plays for BBC Radio include Lethal Cocktails, 1989; Darling Peidi, 1993; The Anatomical Venus, 1994; Five Kinds of Silence, 1996, which received the Writers Guild Award for Best Original Drama; Baby Blue, 1998; Through a Glass, Darkly, 2004; Life is a Dream, 2004; Nemesis, 2005; and The People’s Princess, 2008.
She is also the writer of an occasional therapy comedy series on Woman's Hour called How Does That Make You Feel?, which began in 2010 and reached its 10th season in 2018.
The Memory of Water was made into a film called Before You Go in 2002 starring Julie Walters and Tom Wilkinson and directed by Lewis Gilbert.