He has appeared in the films The Fourth Protocol (1987), Diamond Skulls (1989), Mountains of the Moon (1990), Alambrado (1991), Dirty Weekend (1993), Spy Game (2001), Miranda (2002), Bad Company (2002), Quicksand (2003) and An American Haunting (2005).

In May 1998, Marsh portrayed the character Alex Duncan in the British TV programme As Time Goes By, series 7, episode 3 entitled "The New Neighbours".

He has also appeared in the Red Dwarf episode "Holoship" and the fifth episode of series two of Game On, "Tangerine Candy Floss and Herne Bay Rock" as Brian Kennedy, Mandy's lecherous former university tutor in 1996, as well as portraying Elton John in John and Yoko: A Love Story the 1985 made-for-TV film.

In 2019 Marsh went on to play Jacques De Molay, the ill-fated 14th century Grand Master of the Knights Templar in seven episodes of History's Knightfall.

The two-hander depicted a little-known October 1938 meeting between the future prime minister and Soviet spy Guy Burgess, then a young man working for the BBC.