Firth was a leading child actor by 1970, starring in 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.

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 One film Aces High which featured Firth as the inexperienced RAF pilot Lt. Croft. Coincidentally, Aces High also starred John Gielgud, as well as Malcolm McDowell. The following year, Firth starred in Equus, the film adaptation of the play in which he had starred 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. Subsequent film work has included roles in Lifeforce (1985), The Hunt for Red October (1990) and Pearl Harbor (2001).

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 a BBC dramatisation of the early career of Stephen Hawking.