Torrens was born in Bromley, Kent and educated at Bloxham School in Oxfordshire. He studied English Literature at Trinity College, Cambridge. His television appearances include Consenting Adults, two episodes of Doctor Who ("Human Nature"/"The Family of Blood"), The Brittas Empire, Green Wing, Silk, The Government Inspector (as John Scarlett), The Last Detective and DI Spencer for a few episodes in The Bill in 2001. He has also appeared in a 2008 series of British television advertisements for First Direct, with Matthew King. He appeared also in 1992 episode of Maigret with Michael Gambon