Parker originated the role of Scripps in Alan Bennett's play "The History Boys". He was involved in "The History Boys" from the play's first reading, initially reading the part of Rudge before taking on the role of Scripps in the original London stage production as well as in the Broadway, Sydney, Wellington and Hong Kong productions and radio and film versions of the play. Parker put his musical talents to use in "The History Boys", playing piano and singing in several scenes. His other National Theatre credits include a 2008 revival of "The Revenger's Tragedy".