Born in London, Grant trained at the Central School of Speech and Drama and appeared on stage at the Bristol Old Vic and in the West End of London. One of her best known early roles was as Sarah Francis in British drama Bouquet of Barbed Wire (1976). She has had a successful television acting career. Since 2007, she has appeared on and off in the sitcom Not Going Out, as the mother of Tim (Tim Vine) and Lucy (Sally Bretton).