Curran appeared in the BBC television series This Life. Since then, he has appeared in a number of major film and television roles, including Rodney Skinner (The Invisible Man), an original character in The League of Extraordinary Gentlemen. To portray the Invisible Man, he donned a special suit that turned him into a walking bluescreen. (According to his commentary on the DVD, he looked like a "smurf on acid". ) He also played vampire roles in Guillermo del Toro's Blade II as Priest and Underworld: Evolution as Markus. In 2006 he appeared in the unrated film Red Road.