Kitchen was born in Leicester, Leicestershire. As a young boy (circa 1960) he was head chorister in the Church of the Martyrs choir, where he was a regular soloist. He attended the City of Leicester Boys' Grammar School, where he appeared on stage in a production of Cymbeline.

Kitchen is also a noted actor in British theatre. His roles have ranged from Ptolemy in Caesar and Cleopatra at the Belgrade Theatre in 1966 to Will in Howard Brenton's Magnificence at the Royal Court in 1973 to william Hogarth in Nick Dear's The Art of Success in 1986–87.

He worked with the National Youth Theatre and the Belgrade Theatre in Coventry before attending the Royal Academy of Dramatic Art. In 1969, while still at RADA, he won the "Emile Littler Award" for 'outstanding talent and aptitude for the professional theatre'.

Kitchen was discovered at the Royal Academy of Dramatic Art (RADA) by talent agent Peter Froggatt of Plant & Froggatt Ltd. In the early 1970s, Kitchen appeared in small roles in films such as Unman, Wittering and Zigo (1971) and the Hammer film Dracula A.D. 1972 (1972) before becoming a fixture of British television.

His early TV appearances include roles in Play for Today (Hell's Angels by David Agnew, 1971), Thriller, The Brontes of Haworth, 1973, in which he played Branwell Bronte), Tales of the Unexpected and Beasts. He played the role of Martin in the original 1976 production of Dennis Potter's Brimstone and Treacle, Peter in Stephen Poliakoff's Caught on a Train, Edmund in the BBC Television Shakespeare production of King Lear, the Antipholi in the same series' production of The Comedy of Errors, Private Bamforth in the 1979 BBC television play of The Long and the Short and the Tall, Larner in the film Breaking Glass (1980), Rochus Misch in The Bunker (1981), Berkeley Cole in the film Out of Africa (1985), the King of the United Kingdom in To Play the King (1993), an English land agent during the Irish Famine in The Hanging Gale (1995), and a recurring role as Bill Tanner in the Pierce Brosnan Bond films GoldenEye (1995) and The World Is Not Enough (1999).

He played Mercutio in Romeo and Juliet for the RSC at Stratford and was a member of the National Theatre Company and the Young Vic, where he played Iago in Othello. In 1974 he appeared at Laurence Olivier's National Theatre in the play Spring Awakening opposite Peter Firth, Jenny Agutter, Beryl Reid and Cyril Cusack. Later he appeared opposite Sir Ralph Richardson and Sir John Gielgud in Harold Pinter's No Man's Land, directed by Peter Hall. In 1981 he played Melchior, the manservant of Zangler, in Tom Stoppard's play On the Razzle. In 1984 he played the cabin steward Dvornicheck in Tom Stoppard's play Rough Crossing.

His later films include The Russia House (1990), Fools of Fortune (1990), Enchanted April (1992), The Trial (1993), Fatherland (1994), Doomsday Gun (1994), The Hanging Gale (1995), Kidnapped (1995), Mrs Dalloway (1997), The Railway Children (2000), Proof of Life (2000), Lorna Doone (2001) and My Week with Marilyn (2011).

From 2002 to 2015, Kitchen starred in the ITV mystery-drama Foyle's War as the lead character, DCS Christopher Foyle. He was also a Producer for the show. Other noted appearances include The Buccaneers as Sir Helmsley Thwaite (1995), Dandelion Dead (1994), A Royal Scandal (1996), The Last Contract (Sista Kontraktet,1998) a Swedish film about the assassination of Prime Minister Olof Palme, Paul Abbott's Alibi in 2003, Andrew Davies' dramatisation of Falling in 2005, ITV's three-part drama series Mobile (2007) and Channel 4's phone hacking comedy Hacks (2012).