He served his first role in rep at the Mercury Theatre, Colchester, and his first television appearance was in an adaptation of Mikhail Bulgakov’s The White Guard for the BBC Play of the Month in 1982, and later the Doctor Who story Snakedance in 1983. A sporadic career led to Martin supplementing his income as a photo model for Gilbert and George, and he can be seen in their 1983 work World. Martin got his first regular television role as one of the sons in the BBC sitcom No Place Like Home, and later starred in two series of the sitcom All at No 20.
While Martin was appearing on stage at the Hampstead Theatre, Harry Enfield came to see him; the acquaintanceship developed into a friendship where Martin played characters in Enfield’s sketch shows (most notably one of the Rugby Players). Enfield later recommended Martin for the role of Gary in the sitcom Men Behaving Badly, written for Enfield by Simon Nye, for which Martin received a BAFTA television award for Best Comedy Performance in 1996. Martin played the part of Group Captain Barker in the two-part TV mini-series Over Here that same year. In 1993, Martin played Dick Dobson in Demob about a pair of demobilized soldiers who have to adjust to civilian life following entertaining Second World War troops with a raunchy cabaret act.
Since 1994, Martin has frequently appeared on the BBC One panel show Have I Got News for You as a panelist or a guest presenter. He has since appeared in films and television shows such as An Evening with Gary Lineker, Staggered (starred and directed), Hunting Venus, The Booze Cruise, Saving Grace, and Jeeves and Wooster.