Glen studied at Edinburgh Academy and the University of Aberdeen before honing his craft at the Royal Academy of Dramatic Art, the talented Shakespearian actor would go on to impress audiences in such stage works as Macbeth and Henry V. In 1985, the ascending stage talent made a successful transition to the screen with a small role in an episode of the popular U.K. mystery series Taggart, and after making the leap to the big screen with a supporting role in the 1987 feature Will You Love Me Tomorrow, Glen returned to television the next year for a role in the series The Fear.
In the years that followed, Glen's big-screen career gained notable momentum thanks to solid performances in Gorillas in the Mist (1988) and Rosencrantz and Guildenstern Are Dead (1990), with his early years coming to a peak when he took home a Best Actor award from the Berlin International Film Festival for his turn as a convicted killer in the 1990 film Silent Scream.
He was married to Susannah Harker from 1993 to 2004. They have one son, Finlay. He is now married to Charlotte Emmerson and they have one daughter of nineteen months named Mary.