Barton first gained fame as the original Raoul in the London production of The Phantom of the Opera. He recreated the role in the original Broadway company of the musical and went on to play the lead role of the Phantom for a year. His other theatrical credits include The Red Shoes on Broadway and productions of European productions of Evita, La Cage aux Folles, West Side Story and Jesus Christ Superstar. He also starred as Count von Krolock in the world premiere production of Dance of the Vampires.

Barton is survived by his wife, dancer/choreographer Denny Berry, and his son, Edward.