Lee joined a drama group as a teen. He then starred in the 1997-1998 television adaptation of the Animal Ark books. Aged 16 he started working on Richard III with the Royal Shakespeare Company. Lee appeared in a leading role in the final series of Land Girls (2011) and had several guest roles on television (including Ashes to Ashes, Fresh Meat, Monroe and Henry V). He has also worked on radio (The Emerald Tiger, The Silver Turk and in an adaptation of The Cruel Sea).
Lee was commended in the 2008 Ian Charleson Awards for his appearance in the National Theatre's production of Oedipus and in 2009 played Laertes to Jude Law's Hamlet in the Donmar West End season.
He won first prize of the 2011 Ian Charleson Award for his role as Edgar in the 2010 King Lear production at the Donmar Warehouse.
In 2012 Lee starred in the Donmar Trafalgar Studios production of Aleksei Arbuzov's The Promise.
At Christmas 2013 Lee began a television starring role as DCI Barnaby's new sergeant, DS Charlie Nelson, in the 16th series of Midsomer Murders, which also included the show's 100th episode, partially shot in Denmark in collaboration with the local national broadcasting corporation, DR. In early 2014 he appeared in Versailles at the Donmar Warehouse.
In April 2016 it was announced by ITV that Lee was not returning for season 19 of Midsomer Murders. Lee, on his Twitter account, indicated he would be involved in an upcoming series Jamestown. In August 2017 it was announced that Lee will play Guitarist Brian May in the Queen biopic Bohemian Rhapsody, to be released on 2 November 2018.
