Stevens was born in Croydon, London. He was adopted at birth and grew up in Wales and Southeast England. He has a younger brother who was also adopted. After a rebellious youth, Stevens boarded at Tonbridge School, a private boarding school in Kent, where he became interested in drama after auditioning for the title role in Macbeth with his teacher, novelist Jonathan Smith. From the age of 15, he spent his summers training and performing with the National Youth Theatre in London.

Stevens read English Literature at Emmanuel College, Cambridge.[6] While at Cambridge, he was a member of the Footlights with Stefan Golaszewski, Tim Key, and Mark Watson, and was also active in the Marlowe Society. He was first spotted by director Peter Hall at a Marlowe Society production of Macbeth, in which he played the title character alongside Hall's daughter.