Television

His first television part after drama school was Syd in the Paul Abbott thriller series State of Play, starring John Simm, Bill Nighy and James McAvoy. In 2004, he played Lee in the television film Bella and the Boys. In 2005, he played the 20-year-old version of Giacomo Casanova's son, Giac, in the television adaptation of Casanova, starring David Tennant and Peter O'Toole.^[6]

In 2006, he played Dr. John Seward in the television film Dracula. In 2007, he played Napoleon Bonaparte in an episode of the BBC's docudrama Heroes and Villains and had a small part as a book publisher in the satirical drama The Trial of Tony Blair. In 2009, he played Lieutenant Race in an episode of the 12th series of Agatha Christie's Poirot. In 2011, he played Bentley Drummle in two episodes of the BBC's adaptation of Charles Dickens' Great Expectations. In 2012, he became a regular cast member in the second series of BBC Two's The Hour as journalist Bill Kendall. From 2014 to 2016, he played Athos on the BBC One series The Musketeers, an adaptation of Alexandre Dumas' The Three Musketeers.^[6] He also plays Cormoran Strike in the BBC miniseries Strike, based on the detective novels of Robert Galbraith;^[7][8][9] and Rebrov in Sky TV's The Lazarus Project which will air in the U.S. on the TNT cable network. He played Father Derek 'Dazzle' Jennings, Princess Margaret's friend, in The Crown.^[10]

Film

In 2004, Burke had his first cinema part in The Libertine. In 2007, he played an aspiring filmmaker who ends up directing a porn film in the comedy I Want Candy. In 2008, he played Bluey in Donkey Punch, a horror thriller that debuted at the 2008 Sundance Film Festival. In 2009, he played Geoff Goddard in Telstar: The Joe Meek Story, and had a small part in Stephen Frears' Chéri. In 2010, he played Davy in Third Star, a drama starring Benedict Cumberbatch, JJ Feild and Adam Robertson which follows a trip four friends, one of them terminally ill, make to Barafundle Bay in Wales.^[6]

In 2012, he played Mark in Cleanskin. In 2013, he played Billy, the older brother of Ryan Gosling's character in Only God Forgives, directed by Nicolas Winding Refn. That year he had a supporting role in the Ralph Fiennes-directed film The Invisible Woman.^[6]

In 2020, he played American filmmaker Orson Welles in David Fincher's Netflix original film Mank, opposite Gary Oldman as Herman J. Mankiewicz. He also starred in English director and photographer Mitch Jenkins's 2020 film The Show (written by Alan Moore) as private investigator Fletcher Dennis. In November 2021, Burke joined Anya Taylor-Joy and Chris Hemsworth in the Mad Max: Fury Road spinoff film Furiosa: A Mad Max Saga, replacing Yahya Abdul-Mateen II, who had to drop out due to scheduling conflicts.^[11]

Theatre

As a theatre actor, Burke has worked with the Royal Shakespeare Company and has appeared in plays at Shakespeare's Globe, playing Romeo in Romeo and Juliet in 2004; at the Old Vic in Noël Coward's Design for Living opposite Andrew Scott and Lisa Dillon in 2010; and at the Almeida Theatre playing Greg in reasons to be pretty in 2011. In 2002, he played Hamlet in Howard Barker's Gertrude – The Cry, a reworking of Shakespeare's Hamlet which focuses on the character of Gertrude, the protagonist's mother.^[12]

In 2006, he worked with Ian McKellen in the play The Cut. In 2008, he played Adolph in Creditors at the Donmar Warehouse. Actor Alan Rickman, Burke's godfather, staged the play which earned Burke an Ian Charleson Award. The play subsequently premiered at the Brooklyn Academy of Music in New York in 2010. In 2012, he played Louis Dubedat in The Doctor's Dilemma at the National Theatre.^[13]

Film

Television