Dexter's early successes were on stage, in particular with two high-profile productions of Tennessee Williams plays, beginning with Sam Mendes' 1995 Olivier Award winning production  of The Glass Menagerie at the Donmar Warehouse in which he played Jim O'Connor. This was soon followed by Trevor Nunn's Tony Award winning production  of Williams' never-before-seen Not About Nightingales, which transferred from London's National Theatre to the Circle in the Square Theatre on Broadway in 1999.
Since then, Dexter has moved primarily into film and television. Among an extensive list of British TV credits, he is probably best known in his home country for playing Timothy Gray in the 1950s set ITV crime drama The Bletchley Circle opposite screen wife Anna Maxwell Martin, and for the devious Sun Hill CPS lawyer Matt Hinckley in ITV's The Bill, a role he played from 2006-07.
More recently, in the summer of 2009, Mark returned to the National Theatre in London, playing Robin Conway in Rupert Goold's production of J.B. Priestley's Time and the Conways, he followed this by appearing alongside Kevin Spacey in the role of cynical journalist E.K. Hornbeck, a thinly disguised portrayal of H.L. Mencken, in Trevor Nunn's revival of Inherit the Wind, at the Old Vic.
During the first half of 2010, Mark appeared in the recurring role of businessman Paul Stokes in Coronation Street. He played Count Skriczevinsky in Trevor Nunn's production of Flare Path at the Theatre Royal, Haymarket in 2011. In 2012, Dexter appeared in episode "Trojan" of the Dave series Red Dwarf as Arnold Rimmer's brother Howard.
In December 2012 in the UK (or Jan 2013 in the USA via BBC America) Dexter will appear as the principal villain 'Sir Arthur Donaldson' in the opening episode of the BBC's Victorian crime drama Ripper Street.
On 3 March 2013 Dexter portrayed the celebrated polar explorer Ernest Shackleton in episode 9 of the ITV series Mr Selfridge, and was most recently seen playing CIA Agent 'Marlow' in 24: Live Another Day, which was broadcast in the US and UK in spring 2014.
- Official London Theatre Guide
- Tony Awards.com
- nytimes.com from Allmovie
- Royal National Theatre
- "Photo Flash: Miller, Purefoy & Smith Rehearse Flare Path", February 21, 2011. Retrieved 2011-02-21.