[2] After training at Webber Douglas Academy of Dramatic Art, Kemp received his Equity card when appearing alongside John Thaw and Richard Wilson at the Palace Theatre, Westcliff-on-Sea.

Guest appearances in London's Burning and Birds of a Feather followed, before he had a minor role in the 1987 film Playing Away alongside Neil Morrissey.

The episode, entitled Call Sign Bravo, saw Kemp play the role of Police Constable Dennis Scovell.

[4] Kemp's best-known role is that of hard man Grant Mitchell in the BBC soap opera EastEnders.

Making his debut in February 1990, his character quickly became part of the soap's key storylines during the 1990s, particularly troubled marriages to Sharon Watts (Letitia Dean) and then Tiffany Mitchell (Martine McCutcheon), as well as the "Sharongate" storyline, which saw brother Phil Mitchell (Steve McFadden) having an affair with Grant's wife, which was uncovered two years after it began.

In January 2016, it was confirmed that Kemp would make a brief return to the show for the death of Grant's on-screen mother, Peggy Mitchell (played by Windsor), appearing in three episodes during May of that year.

[7] Following his initial departure from EastEnders, Kemp moved from the BBC to ITV for a reported £1.2 million two-year deal.

He took the lead roles in the television series Without Motive and In Defence in 2000, and in 2002's Ultimate Force, where he played Army Staff sergeant Henry Garvie from the British Special Air Service.

In 2005, Kemp appeared in an episode of BBC's Extras and in a two-part adaptation of the Gerald Seymour novel A Line in the Sand for ITV.

In 2022, Kemp began presenting the game show Bridge of Lies, airing on weekdays on BBC One,[10][11] as well as a series of celebrity specials broadcast on Saturday evenings.

[citation needed] In September 2023, Kemp released Take Nothing For Granted: Tales from an Unexpected Life; a retrospective look back at his career.

[19] In October 2000 the Glasgow University Students' Representative Council passed a motion requesting him to resign,[20] and within weeks he did.

[21] Kemp was the first rector in 50 years to leave the position prematurely and was succeeded by Scottish actor Greg Hemphill.

[19][22] In August 2014, Kemp was one of 200 public figures who were signatories to a letter to The Guardian opposing Scottish independence in the run-up to September's referendum on that issue.