Moore trained at Guildhall and made his screen debut in Stephen Fry's Bright Young Things. He is primarily a stage actor, and has performed with the RSC.

Moore played the role of Irwin in the original West End stage production of Alan Bennett's play The History Boys, and also played the character in the Broadway, Sydney, Wellington and Hong Kong productions and in the film version of the play.

Moore was nominated for a 2006 Drama Desk Award for his work on the Broadway production of The History Boys.