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
In 2011, Torrens appeared in both episodes of an Outnumbered two-part special. In 2012 he appeared in the first episode of series 8 of Hustle as Heinz Zimmermann and also presented new gameshow The Devil's Dinner Party. Torrens briefly appeared in an episode of Death in Paradise in 2013, as a museum guide. His film appearances include Tomorrow Never Dies as the captain of HMS Bedford, the 2001 film To End All Wars and voicework for Valiant. He also does work as a simulated patient in medical schools in the UK.
In 2013, Torrens appeared in "The Waldo Moment", an episode of the anthology series Black Mirror.
In November 2014, Torrens played the part of Richard Grenville in the BBC Radio 4 drama The Archers.
