Graves got his start in show business as a plate-spinning clown with a traveling circus. He made his acting debut as a regular on the British series "Vice Versa" (1980-81) and went to appear as an English officer in support of Kenneth Branagh and Emma Thompson in the BBC series "Fortunes of War" (1988; shown in the USA on PBS' "Masterpiece Theatre").
On stage, Graves made his debut in "The Killing of Mr. Toad" (1983) and appeared in the London premiere of "Torch Song Trilogy" (1984), opposite Harvey Fierstein, and Martin Sherman's "A Madhouse in Goa" (1989), opposite Vanessa Redgrave. He was twice directed by "A Room With a View" co-star Simon Callow, in the title role of "Amadeus" and in the 1995 stage version of "Les Enfants du Paradis" (1995).
But Graves has made the biggest impact on film. Following his debut, he was featured in the Merchant-Ivory production of "Maurice" (1987), as the working-class game keeper who seduces the title character (James Wilby). In Charles Sturridge's "A Handful of Dust" (1988), based on the Evelyn Waugh novel, Graves was John Beaver, the penniless socialite who begins an affair with his host's wife (Kristin Scott Thomas) with dire consequences. He reteamed with Sturridge for "Where Angels Fear to Tread" (1991), another costume drama in which he romanced Helena Bonham Carter. His first modern role in films was as Jeremy Irons' journalist son in Louis Malle's "Damage" (1992). Graves returned to period fare as the monarch's equerry in "The Madness of King George" (1994). In 1995, he delivered an excellent portrayal of an irresponsible young man who rekindles a relationship with a former classmate in the offbeat "Different for Girls". The same year, he won praise as a homeless alcoholic who witnesses a murder in the thriller "The Innocent Sleep". Graves also gained kudos for his turn as a drifter who begins an affair with a much older married woman (Julie Walters) with tragic consequences in the based-on-fact black comedy "Intimate Relations" (1996). Graves reteamed with Bonham Carter and Scott Thomas for "The Revengers Comedies" (1997) and was in support of Vanessa Redgrave in Marleen Gorris' "Mrs. Dalloway" (also 1997).