In 2012, Beevers appeared as Fray Antonio in the Royal Shakespeare Company production of Helen Edmundson's The Heresy of Love.
From October 2016 to March 2017, he played Baron Gottfried Van Swieten in a production of Amadeus by Peter Shaffer at the Royal National Theatre's Olivier Stage.
In 1988 he appeared in the TV movie sequel The Great Escape II: The Untold Story, and played Wainwright (Member of Parliament) in A Very British Coup for Channel 4 Television (UK).
In 1993, Beevers appeared as Inspector Montgomery in The Case-Book of Sherlock Holmes feature length episode The Eligible Bachelor.
Beevers narrated the unabridged audio edition of Doctor Who: Harvest of Time, by Alastair Reynolds, released in June 2013.