Parker was born in London, England, the son of the former British Rail chairman Sir Peter Parker and Lady Jillian Parker, a writer. He was educated at Fox Primary School, Colet Court and Leighton Park School in Reading, Berkshire. Parker's brother is the film director Oliver Parker. He also has another brother, Alan Parker, who is chairman of Brunswick Group Ltd. Parker is married to actress Anna Patrick. The couple live in London with their daughters Raphaella (born 1998) and Angelica a budding actress (born 1996).

Parker joined the National Youth Theatre, and after training at The London Academy of Music and Dramatic Art, became a member of the Royal Shakespeare Company. He portrayed Bassanio in Peter Hall's 1989 production of The Merchant of Venice in both London and on Broadway, co-starring with Dustin Hoffman. In 2000, he played Bob in Rupert Goold's West End revival of David Mamet's Speed-the-Plow. "With his unforced, tough demeanour and conviction Parker substantially carries the evening", wrote John Thaxter in The Stage (6 July 2000).

In a Radio Times interview in 2007, Parker said that his first big television break came in 1988 when he played a Battle of Britain pilot in ITV's glossy six-part drama Piece of Cake. Other early roles include playing Wilfred Owen in Derek Jarman's 1989 film adaptation of War Requiem, which also starred Laurence Olivier as an old soldier in his last screen role before his death, and playing Edward Rochester in John Duigan's 1993 film adaptation of Jean Rhys' Wide Sargasso Sea.

Parker established his reputation by playing a variety of television costume drama roles, such as Martin Jordan in the 1995 TV production of Joanna Trollope's A Village Affair, Gabriel Oak in the ITV production of Far From the Madding Crowd (1997), Rawdon Crawley in a BBC version of Vanity Fair (1998), and recently and most notably Harold Skimpole in the BBC1 dramatisation of Bleak House (2005).

From 2001 through 2007, Parker played Detective Inspector Lynley in the long-running BBC1 thriller series The Inspector Lynley Mysteries, co-starring with Sharon Small who plays his sidekick Det. Sgt. Barbara Havers. He has also played Edward Gracey in Disney's 2003 film adaptation of The Haunted Mansion (film), Albert Speer in the 2006 BBC production Nuremberg: Nazis on Trial, Dunstan Thorne in the 2007 fantasy film Stardust.

Parker is also a voiceover artist and has done work in audio books including Eoin Colfer's children's Artemis Fowl series (the latest installment of which - Artemis Fowl: The Time Paradox - Parker has recorded, but no release date has been announced), Young James Bond adventure, Silverfin by Charlie Higson and The Gardens of The Dead by William Brodrick. He also read Mark Haddon's novel A Spot of Bother for BBC Radio Four's Book at Bedtime.

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