His television performances include roles in the BBC comedy Twenty Twelve and in the Showtime drama Penny Dreadful.

[7] In 2009 Barnett played John Everett Millais in the BBC series Desperate Romantics and Joseph Severn in the film Bright Star.

[11] In 2022 at the Edinburgh Fringe, Barnett performed a one-man show Feeling Afraid as If Something Terrible Is Going to Happen written by Marcelo dos Santos.

He won Best Newcomer and Best Supporting Actor in a play at the Whatsonstage.com Theatregoers Choice Awards for his work on the original production of The History Boys.

[18] In 2022 Barnett received the Stage Edinburgh Award for excellence in acting for his role in the solo-show Feeling Afraid As If Something Terrible Is Going To Happen.