Bradley was born in York, where he attended the Catholic St George's Secondary Modern School, at which he was a member of the choir. He first performed on stage in musical productions as a member of a youth club and with the Rowntree Youth Theatre. Upon leaving school he completed a five-year apprenticeship with the optical instruments maker Cooke, Troughton & Simms and he remained with the firm until 1966 when he moved to London to train as an actor at the Royal Academy of Dramatic Art.
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.
Bradley played fictional Labour Member of Parliament Eddie Wells in the 1996 award-winning BBC Two serial Our Friends in the North. In 1996, he appeared as gangster Alf Black in Band of Gold. In 1998, he appeared in the BBC adaptation of Vanity Fair as the miserly Sir Pitt Crawley, and Our Mutual Friend as the villainous Rogue Riderhood. Other television appearances include the 2001 series The Way We Live Now, directed by David Yates, who would work with Bradley five years later on the Harry Potter films.
From 2002–04, Bradley starred as Jake in the BBC comedy series Wild West. Bradley acted in the 2004 musical drama serial Blackpool on BBC One. He appeared in the 2005 BBC drama Mr. Harvey Lights a Candle, playing the role of a morose coach driver who takes an unruly party of pupils on a trip to Salisbury Cathedral, and the 2006 BBC drama Sweeney Todd. He had a small role in a 2006 episode of the series Taggart. In 2003, he played Tom in the Midsomer Murders episode "The Green Man". He appeared as the electrolarynx-using gangster Stemroach in the BBC comedy series Ideal and as Electric in the BBC's Thieves Like Us, as well as the BBC One series True Dare Kiss in 2007–08.
Bradley appeared in the 2002 film Nicholas Nickleby, and had a small role in the 2007 comedy film Hot Fuzz as a farmer who illegally hoards weapons. He played Cohen the Barbarian in a Sky One adaptation of The Colour of Magic in 2008. That same year he appeared as Spooner in a production of No Man's Land at the Gate Theatre, Dublin, which later transferred to London's West End.
In 2009, Bradley appeared as an animal rights activist in the popular BBC drama Ashes to Ashes, and appeared in BBC's The Street later that year. Bradley portrayed Will Somers, Henry VIII's court fool, in an episode of the Showtime series The Tudors in 2009. In 2010, he appeared in the film Another Year, which earned him a nomination for Best Supporting Actor from the London Film Critics Circle Awards. In 2011, 2013 and 2016, Bradley appeared as Lord Walder Frey in the HBO series Game of Thrones. In January 2017, it was confirmed that Bradley would appear in the seventh season of the show later that year.
Bradley played Solomon, a ruthless buccaneer, in the 2012 Doctor Who episode "Dinosaurs on a Spaceship". He previously provided voice work for The Sarah Jane Adventures serial Death of the Doctor. It was announced in January 2013 that Bradley had been cast as actor William Hartnell in An Adventure in Space and Time, a BBC docudrama about the creation of Doctor Who in 1963. The special aired in November 2013, adding to the buildup to the 50th anniversary episode of Doctor Who later that month.
From 2014, Bradley plays Professor Abraham Setrakian, a Holocaust survivor turned vampire hunter in Guillermo del Toro's TV series The Strain. He will voice the Lord High Admiral Suvarov in the PC RPG The Mandate.
In 2015, Bradley was announced a public supporter of Chapel Lane Theatre Company based in Stratford-Upon-Avon, UK.
In 2017, in the final episode of the tenth series of Doctor Who, "The Doctor Falls", Bradley returned to portray the First Doctor, having previously portrayed Hartnell, who originally played the character. He will reprise this role in the 2017 Christmas Special, "Twice Upon a Time". This makes him the third actor to play the role in the television programme, after William Hartnell and Richard Hurndall since the premiere of Doctor Who in 1963, and at the age of 75, he is the also the oldest actor to play the role of the Doctor.
Bradley serves as the President of Second Thoughts Drama Group, which performs in and around Stratford-upon-Avon. On 17 July 2012, he was awarded an Honorary Doctorate from the University of Warwick. On 19 November 2015, he was awarded an Honorary Doctorate from York St John University.
He is an avid fan of football clubs Aston Villa and York City. On 22 November 2014, he took part in a video paying tribute to Aston Villa on the club's 140th birthday.