[10] His early work included small roles in Agent Cody Banks 2: Destination London, directed by his uncle, the film Atonement, and in BBC1's historical hospital drama, Casualty 1907, as Nobby Clark.

[4][14][15] Allen came to international attention when he was cast as Theon Greyjoy in the HBO fantasy series Game of Thrones, an adaptation of George R. R. Martin's A Song of Ice and Fire, in 2011.

[21] That same year, he played Ringwood in the BBC Two 1940s-set miniseries Close to the Enemy and joined the London production of Jesse Eisenberg's The Spoils at Trafalgar Studios.

[22] Allen co-starred in the sci-fi sequel The Predator as Lynch in 2018, and Taika Waititi's Oscar-nominated dark comedy Jojo Rabbit as Finkel as well as the coming-of-age film How to Build a Girl as John Kite in 2019.

Allen made his Broadway debut in 2022 when he took over the role of Mooney from Dan Stevens in Martin McDonagh's Hangmen at John Golden Theatre.