Graves first gained notice in the 1980s with key roles in the Merchant-Ivory films Room with a View and Maurice (as James Wilby's lover). Other period dramas followed, including Where Angels Fear to Tread (directed by Charles Sturridge), The Madness of King George, and Mrs. Dalloway. In a departure from historical fare, he played Dominic in the dystopian graphic novel adaptation V for Vendetta. On television, he starred as Young Jolyon in the Masterpiece Theater co-production The Forsyte Saga and played Lestrade on Sherlock.