 In the same year he had a supporting role in the Ralph Fiennes-directed film "The Invisible Woman".As a theatre actor, Burke has worked with the Royal Shakespeare Company and has appeared in plays at Shakespeare's Globe, playing Romeo in "Romeo and Juliet" in 2004; at the Old Vic in Noël Coward's "Design for Living" opposite Andrew Scott and Lisa Dillon in 2010; and at the Almeida Theatre playing Greg in "reasons to be pretty" in 2011.In 2002 he played Hamlet in Howard Barker's "Gertrude – The Cry", a reworking of Shakespeare's "Hamlet" which focuses on the character of Gertrude, the protagonist's mother.