After graduating Davies was cast by the theatre director Dominic Cooke at the Royal Court Theatre, where he won a Laurence Olivier Award for Most Promising Performer for his portrayal of Danny in Grae Cleugh's Fucking Games. He then appeared at the Traverse Theatre to work with Wilson Milam, then to the National Theatre Studio. He played "Dill" in Harper Lee's To Kill a Mocking Bird. Later that year he worked with the avant-garde film director Peter Greenaway on The Tulse Luper Suitcases, Part 1: The Moab Story with Debbie Harry and The Tulse Luper Suitcases, Part 2: Vaux to the Sea with Isabella Rossellini.
He played Dominic Morrison in Sea of Souls for BBC television drama, then played Lawrence in the first ever production of Lovely Evening by Peter Gill, for Daniel Evans' directorial début at the Young Vic Theatre. Later that year, he joined the Oxford Stage Company, appearing in Rookery Nook by Ben Travers for Dominic Dromgoole's final show with the OSC. Davies played Mickybo in Mojo Mickybo by Owen McCafferty at the Trafalgar Studios in the West End theatre.
His first Hollywood role was in Fast & Furious 6. He returned to the stage for the National Theatre of Scotland in the John Tiffany production of Black Watch which toured the UK, USA and to South Korea. He returned to television screens for the crime drama Suspects. Davies went on to work with the American Israeli contemporary video artist Omer Fast on his first feature film Remainder by British author Tom McCarthy. He returned to the American stage in Los Angeles to work with Steven Berkoff on his production of The Hairy Ape by Eugene O'Neill in 2016.