Born in Westminster in 1945, but brought up in the Midlands, Fraser studied acting at the Webber Douglas Academy of Dramatic Art and the London Academy of Music and Dramatic Art. As a member of folk band Telltale, Hugh co-wrote and performed the theme music for Rainbow, the iconic ITV children's television series.

Fraser's first big break came after portraying Anthony Eden in the 1978 television series Edward & Mrs. Simpson, with Edward Fox, after which he was frequently cast as upper class or aristocratic characters, such as Mr Talmann in Peter Greenaway's The Draughtsman's Contract.

His film credits include Curse of the Pink Panther, 101 Dalmatians and Patriot Games along with his Sharpe co-star Sean Bean. He has also worked in theatre, playing Claudio in Much Ado About Nothing with the Royal Shakespeare Company in 1979. He has guest starred in the Doctor Who audio dramas Circular Time (2007) and Cradle of the Snake (2010), and in 2003, alongside Martin Shaw in Death in Holy Orders.

In the 1980s, he appeared in the BBC thriller Edge of Darkness. Fraser can be frequently heard narrating the audiobooks of Christie's works, which are currently published by HarperCollins publishers. As of recent years, he has been an associate tutor, Director and member of the audition panel at the Royal Academy of Dramatic Art, specialising in Shakespeare. Fraser has also directed several plays, most notably a production of David Mamet's adaptation of Chekhov's Uncle Vanya, which was staged at Wilton's Music Hall in London in January 2007, with Rachael Stirling as Yelena.

Fraser has also become an author; his first novel, Harm, was published in 2015, followed by Threat in 2016. The third in the Rina Walker series, Malice, came out in October 2017.