Torrens was born and raised in Kent, England.He attended Bloxham School in Oxfordshire and then studied English Literature at Trinity College, Cambridge.
Torrens first notable role was as Thomas in the 1986 film Lady Jane. Torrens has since starred in many well known films, such as Pride and Prejudice in 2005, My Week with Marilyn in 2011 and War Horse. In 2012, he starred in Anna Karenina and in 2015, he had roles in The Danish Girl and Star Wars: The Force Awakens.
Torrens has also starred in many TV roles. He starred in two episodes of Doctor Who, and will portray Tommy Lascelles in the 2016 series The Crown. Since 2015, he has starred in the BBC adapation of Poldark as Cary Warleggan.