Graves first came to prominence in costume-drama adaptations of E. M. Forster's novels A Room with a View (1985), and Maurice (1987), before going on to appear in films including A Handful of Dust (1988), The Madness of King George (1994), Different for Girls (1996), and Intimate Relations (1996). Graves's role in Intimate Relations won him the Best Actor award at the 1996 Montreal World Film Festival. He was also acclaimed for his portrayal of Young Jolyon Forsyte in the television miniseries The Forsyte Saga.
Later, he appeared in films such as V for Vendetta (2005), Death at a Funeral (2007), Horrible Histories: The Movie – Rotten Romans (2019), and Emma (2020), and in TV series such as Charles II: The Power & the Passion (2003), A Waste of Shame (2005), Sherlock (2010–), The Crimson Field (2014), and The Family (2016).