Kay was born in Edinburgh and transracially adopted as a baby and raised in Glasgow. She graduated in English from the University of Stirling in 1983.
She is the author of The Adoption Papers, Chiaroscuro, Twice Through the Heart, a biography, Bessie Smith, a novel, Trumpet, and a collection of short stories, Why Don't You Stop Talking.. The Adoption Papers won the Eric Gregory, Saltaire and Forward awards.
She lives in Manchester with her partner, poet Carol Ann Duffy, and their two children.
She has traced her birth mother but does not discuss it.