Bradley joined the Royal Shakespeare Company and performed at Laurence Olivier's National Theatre Company in the early 1970s. He first appeared on television in 1971, as a police officer in the successful comedy "Nearest and Dearest". He was awarded a Laurence Olivier Award in 1991 for his supporting role as the Fool in "King Lear" at the Royal National Theatre. He appeared in the Royal National Theatre's 1997 production of "The Homecoming", as well as productions of "The Caretaker" at Sheffield Theatres and the Tricycle Theatre from 2006 to 2007. In 2005 he played the title role in Nicholas Hynter's production of Henry IV Parts One and Two at the Olivier Theatre, London.