Martin's work at the National Theatre and National Theatre of Scotland includes Our Ladies of Perpetual Succour (West End and International), War Horse, Pinocchio, The Light Princess, Caroline or Change, Jerry Springer The Opera, The Wolves in the Walls, Appointment with the Wicker Man and Earthquakes in London.
At the Royal Court, his works include After The Act, Sound of the Underground, The Twits, and Jack Thorne’s Hope (Royal Court), Jedermann and Mackie Messer for the Salzburg Festival. Martin was the Music supervisor for Abba Voyage at the Abba Arena, and Musical Director for Mamma Mia! The Movie, and the Thames TV series I Have a Dream.
Other West End shows include Cats, Les Misérables, The Full Monty, and Once on this Island.
He won the Tony, Grammy, Olivier, Drama Desk and Helpmann award for his work on the musical Once, and a Golden Reel Award for Mamma Mia! The Movie.