Graham is an experienced theatre director.

Graham was the recipient of the Rose Bruford Trust Director’s Award and he has directed around 130 professional productions, 28 of them by Shakespeare. Companies he has worked for include the Royal Shakespeare Company, Globe Theatre, English Shakespeare Company, National Theatre of Great Britain, Royal Academy of Dramatic Art, the Mercury Theatre, Colchester, where he was Associate Director, Hull Truck, Fairbanks Shakespeare Theatre, Alaska, and the English Theatres in Hamburg, Frankfurt, and Vienna. His productions have played in New York and at the World Shakespeare Congress in Brisbane, Australia.

In 2021, Graham started a youtube channel called "Lost Ladies (found)" which takes plays that were written by brilliant women but perhaps ignored due to gender bias, and recreates them for online audiences.