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Bradley became an actor in 1971, first appearing on television that year in the successful comedy Nearest and Dearest playing a police officer. He was awarded a Laurence Olivier Award in 1991 for his supporting actor role in King Lear at the Royal National Theatre. He has appeared in the Royal National Theatre's 1997 production of Harold Pinter's The Homecoming, as well as productions of Pinter's The Caretaker at Sheffield Theatres and the Tricycle Theatre in London in 2006/2007.
Bradley starred in the BBC comedy series Wild West playing the character of Jake. He played fictional Labour MP Eddie Wells in the 1996 award-winning BBC Two serial Our Friends in the North. Other television appearances include the 2004 musical drama serial Blackpool on BBC One, the 2005 BBC television drama Mr. Harvey Lights a Candle, playing the part of the morose coach driver taking an unruly party of pupils on a daytrip to Salisbury Cathedral and the 2006 BBC drama Sweeney Todd, playing the father of opposite Ray Winstone, and a small part in a 2006 episode of the series Taggart. Also in 2006 he played a leading character, Tom, in an episode of Midsummer Murders. He also appears as the character Stemroach in the BBC comedy series Ideal and as Electric in the BBC's Thieves Like Us, and in the BBC1 series True Dare Kiss.
Bradley appeared in Nicholas Nickleby (2002) and had a small role in the 2007 comedy film Hot Fuzz as a farmer who illegally hoarded weapons, including a sea mine which later proves important to the story.
Bradley played Cohen the Barbarian in a Sky One adaptation of The Colour of Magic by Terry Pratchett.
In 2008 Bradley appeared in the role of Spooner in No Man's Land by Harold Pinter in the Gate Theatre, Dublin, opposite Michael Gambon as Hirst, in a production directed by Rupert Goold, which transferred to the London West End's Duke of York's Theatre, for which roles each received nominations for the 2009 Laurence Olivier Award for Best Actor, to be announced on 8 March2009; if he wins, it would be Bradley's first Olivier award in that category; if Gambon wins, it would be his second.
In 2012, Bradley portrayed the 24th century pirate Solomon in the Doctor Who episode Dinosaurs on a Spaceship.