Firth was born in Bradford, Yorkshire, England, the son of Mavis (née Hudson) and Eric Macintosh Firth. He has four children named Rory, Amy, Alex and James.

Firth was a leading child actor by 1970, starring in the Flaxton Boys as Archie Weekes and a television series called Here Come the Double Deckers, which featured British child actors in the leading roles. Firth played Scooper, the leader of the gang.

In 1973, he starred in the London stage version of Peter Shaffer's play Equus, playing a teenager being treated by a psychiatrist, and repeated the role in the Broadway production, receiving a Tony Award nomination for his performance as Alan Strang.

His first major role as an adult was in the title role in a 1976 BBC Television Play of the Month adaptation of Oscar Wilde's novel The Picture of Dorian Gray. The adaptation was scripted by John Osborne and also starred Jeremy Brett and John Gielgud, becoming a major success with the critics.

That same year saw the release of the World War I film Aces High which featured Firth as the inexperienced RFC pilot Lt Croft. Aces High also starred John Gielgud, as well as Malcolm McDowell.

The following year, Firth starred in the film adaptation of Equus, the play in which he had starred in London and on Broadway. The film was a success and earned Firth a nomination for the Academy Award for Best Supporting Actor and victory in the same category at the Golden Globe Awards. Further film work quickly followed, most notably Roman Polanski's Tess (1979), an adaptation of Thomas Hardy's novel Tess of the D'Urbervilles.

In parallel to his film career, Firth has continued to appear in various television productions, with several notable credits in various high-profile dramas.

In 1980 he starred as the eponymous time traveller in the BBC's feelgood science-fiction play The Flipside of Dominick Hide, and two years later starred in a sequel, Another Flip for Dominick. Both of these were made as part of the BBC's famous Play for Today anthology drama strand.

More recently, he has starred as senior MI5 officer Harry Pearce in the BBC's popular spy drama series Spooks (2002-present), and played Fred Hoyle in Hawking, a BBC dramatisation of the early career of Stephen Hawking.