Television
Burnet joined the cast of Hollyoaks in 2002 as Craig Dean, a main character. During his time on the show, he was central to a popular and culturally significant storyline involving his character’s relationship with John Paul McQueen, which remains one of the most talked-about and ground breaking arcs in the show's history. On 3 August 2007, producer Bryan Kirkwood confirmed Burnet's departure, calling him "an amazing actor" and noting that "he has really come into his own."
In 2009, Burnet played "Pinklady" in Moving On for the BBC. After several years on the New York stage, Burnet transitioned into U.S. television and film. He appeared in the Showtime drama Ray Donovan, and later joined the third season of The Affair in the recurring role of Mike Cornwell.
In 2017, Burnet joined the second season of Amazon's Hand of God starring Ron Perlman. He also appeared in Counterpart opposite J.K. Simmons.
He was also featured in the Bryan Cranston–produced Amazon series Philip K. Dick's Electric Dreams alongside Terrence Howard and Anna Paquin.
Burnet later led the cast of the Amazon-BBC sci-fi drama The Feed, based on the novel by Nick Clark Windo. He played Tom Hatfield, a psychologist navigating a world shaped by implanted technology, with David Thewlis playing his father. The series drew praise for its eerie relevance and Burnet’s grounded performance in the lead role.
More recently, Burnet stars as Chips in the Netflix action-comedy series FUBAR alongside Arnold Schwarzenegger. His portrayal of Chips — a character brought to life through a blend of vulnerability, bravado, humor, and intensity — was noted for its distinctive charisma and earned praise as a standout performance.
In 2025–2026, Burnet appeared as Charlie Newsom in the Paramount+ drama series Landman, created by Taylor Sheridan, alongside Billy Bob Thornton. The series became one of most-watched original programmes, drawing record viewership for the platform during its run.
