Parker joined the National Youth Theatre, and after training at the London Academy of Music and Dramatic Art,[2] became a member of the Royal Shakespeare Company in 1986.

[6] Parker returned to the stage in 2013 for the production of The Audience, starring Helen Mirren, written by Peter Morgan and directed by Stephen Daldry.

[15] In a 2007 Radio Times interview, Parker said that his first big television break came in 1988 when he played a Battle of France pilot in ITV's six-part drama Piece of Cake.

"[19] At the same time, he played Master Gracey in The Haunted Mansion,(2003),[20] Albert Speer in the BBC production of 2006 Nuremberg: Nazis on Trial[21][22] and Dunstan Thorn in the fantasy film Stardust (2007).

[25] He also appeared as Chief Inspector Armand Gamache of the Sûreté du Québec in the film adaptation of Louise Penny's murder mystery novel Still Life, set in rural Quebec.

[2] In July 2015, Parker played the domestic bully Dicky Carmichael in the BBC's two-part television adaptation of Sadie Jones' debut novel The Outcast.

[28] In 2018, Parker appeared in two films, firstly as King Hamlet (better known as the Ghost), in Ophelia opposite Daisy Ridley, then as Lewis in the sports comedy-drama Swimming with Men.

He also played Lord Chiltern in Oscar Wilde's An Ideal Husband at the Vaudeville Theatre; the production received positive reviews from critics and was later broadcast in cinemas.

[29][30][31] In 2019, he played civil servant Sir Robert Hamilton in The Warrior Queen of Jhansi, a period drama about the life of Rani Lakshmi Bai, one of the leading figures in the Indian Rebellion of 1857.

[32] In 2021, Parker appeared on television in Spanish-language romantic drama series The Vineyard as Edward Clayton, as well as ITV thriller The Beast Must Die.

On television, he featured in Paramount+ period thriller The Doll Factory as Liston, and guest starred in one episode of Midsomer Murders, playing Brian Havergal.