Burnet attended Holland Park School where his interest in drama first developed, taking an A level in the subject.

[5][6] Burnet joined the cast of Hollyoaks in 2002 as a main character and series regular, Craig Dean, following his second ever audition.

[12] He was seen in the Bryan Cranston produced Amazon series Philip K. Dick's Electric Dreams opposite Terrance Howard and Anna Paquin.

Other roles include work in Boxing Day, a Leo Tolstoy adaptation directed by Bernard Rose, in the thriller Rites of Passage with Christian Slater and Stephen Dorff, and in Age of Heroes a period war film with Sean Bean.

[14] Burnet then went on to play Ewan McGregor's partner in crime caper Mortdecai opposite Johnny Depp.

His interest in boxing led him to direct a documentary on WBU featherweight title holder Derry Mathews.