Originally from Manchester, he took some classes in theatre school but received the bulk of his training as an apprentice with the Hull Truck Theatre. He performed his Cockroach trilogy of one-man plays (The Cockroach That Ate Cincinnati, The Return of the Cockroach and The Cockroach Has Landed) at the International Theatre Festival in Toronto, Ontario in 1981, and then decided to remain in the city, becoming playwright in residence at the Tarragon Theatre.
His subsequent plays in Canada included The Warlord of Willowdale, The White Dogs of Texas, King of America, Dixieland's Night of Shame, Welcome to the NHL and The Duke of Nothing. He also took some acting roles in other playwrights' work, most notably appearing opposite Linda Griffiths in her two-person play The Darling Family and its 1994 film adaptation by Alan Zweig.
Soon after completing The Cockroach that Ate Cincinnati, Williams moved back to England, where he has had roles in films such as The Scold's Bridle, Touching Evil, The Life and Death of Peter Sellers and Vera Drake, and television series including Always and Everyone, Coronation Street, Wire in the Blood, Life Begins, The Virgin Queen, Rome, Luther and Starlings.