Burns was born in Liverpool, England. When Burns was 11 her grandmother sent her to acting classes. From there she received a part in the film Liam (2000). She won the Marcello Mastroianni Award at the Venice Film Festival for her performance. Danny Boyle saw this and cast her in his film 28 Days Later, where she played Hannah, one of the survivors of a deadly epidemic. Megan was cast in the film In2ruders, directed by Naeem Mahmood, also starring Tony Hadley and Caprice Bourret.