Her breakthrough performance was in "A Room with a View" in 1985, when she played Lucy Honeychurch. Carter also appeared in episodes of "Miami Vice" as Don Johnson's love interest during the 1986-87 season. She auditioned for the role of Nancy Spungen in "Sid and Nancy" in 1986, but lost the role to Chloe Webb. These early roles led her to be typecast as a "corset queen", and "English rose." She expanded her acting range in more recent movies like "Fight Club", "Wallace & Gromit: The Curse of the Were-Rabbit", and in Tim Burton's "Charlie and the Chocolate Factory", "Corpse Bride", "Big Fish", and "Sweeney Todd".