Addy made his first television appearance in 1987 in
The Ritz, followed in 1988 by
A Very Peculiar Practice, followed by television performances in shows such as
Heartbeat, He portrayed Bill Miller (using an improvised American accent) in the CBS sitcom
Still Standing from 2002-2006 (88 episodes) and portrayed Detective Boyle in the second series of the British sitcom
The Thin Blue Line. He also appeared on
ITV1's comedy drama series
Bonkers, and another ITV comedy drama,
Bike Squad, in early 2008 as Sergeant John Rook. In 2011, He portrayed King
Robert Baratheon in the HBO series
Game of Thrones: Addy's audition for the role was, according to showrunners
David Benioff and
D. B. Weiss, the best they saw, he being the easiest actor to cast for the show. Although Robert was a main character in the series beginning, the king's enthusiasm for a "drinking, whoring, and fighting" eventually took its toll, and Addy's character was killed off in season 1 after a hunting incident with a wild boar. He portrayed
Hercules, one of the main characters in the
BBC One fantasy drama series
Atlantis, which started airing on 28 September 2013 in the UK. In the BBC television drama
New Blood (2016), In film, Addy had a leading role in
The Full Monty (1997), and portrayed
Fred Flintstone in the 2000 film
The Flintstones in Viva Rock Vegas. In 2001, he portrayed Roland in ''
A Knight's Tale'' and a butler to
Chris Rock's character in the film
Down to Earth. In
Down to Earth, his character was an American who was pretending to be British. Addy portrayed David Philby in
The Time Machine In 2019, he appeared in the
Downton Abbey movie as Mr. Bakewell, who owns the shop from which Mrs. Patmore buys her supplies; a character who was mentioned in the television series but hadn't yet appeared onscreen. In 2020, he portrayed DS Stan Jones in the detective drama series
White House Farm. In 2023, Addy starred as David Coake, causing issues on the Kinloch Bravo oil rig in
The Rig, in a cast that included
Iain Glen,
Emily Hampshire, and
Martin Compston.
Stage Addy portrayed Kevin Snell in the 2006 revival of ''
Donkeys' Years at the Comedy Theatre in London. In 2007–08 he has appeared at the National Theatre as Dogberry in Much Ado About Nothing alongside Zoe Wanamaker, and as Hjalmar Johansen in the Tony Harrison play Fram'', also at the
Royal National Theatre. In 2011, he portrayed Vladimir, an
NKVD officer, in
Collaborators at the
National Theatre, ==Honours==