Born in Edinburgh, Cavanah lives in England, the father of two. He attended James Gillespie's High School in Edinburgh. He left the Royal Scottish Academy of Music and Drama in 1986, after just one term, but later graduated from a three-year acting course at Drama Centre London in 1994, part of the University of the Arts London.

Starring roles include Cracker, Blue Dove, Cadfael, Hamish MacBeth, Kavanagh QC, Rose and Maloney, Rebus, Silent Witness, Highlander: The Raven, Casualty, DCI Banks, Waterloo Road, The Bill, The Governor, The Borgias and Hatfields and McCoys. He played Adam Carnegie in the ITV1 drama series The Royal for three series and played Tommy Grant in the BBC1 soap opera EastEnders. He starred in the 1998 ITV version of Wuthering Heights as Heathcliff. He played Ian in Emmerdale and guest starred on the second series of Outlander shot in 2015.

Cavanah wrote, produced and directed the following short films: Soldier's Leap (1999), Fish (2001), and Trumps (2001). He made his directorial feature debut in Pimp which he wrote and in which he also starred. He wrote the feature films Invisible and Wreckage. As of 2015, he was working on a first novel and stage play.

He appeared at the Royal National theatre in 2010/11 in the Ena Lamont Stewart play Men Should Weep in the role of John Morrison alongside Sharon Small. He played the title role in MacBeth at the Octagon Theatre, Bolton, directed by David Thacker (February 2012). In 2015-16, Cavanah played John Churchill in the RSC's production of Helen Edmundson's Queen Anne and Scandal in the RSC production of Love for Love.