Born in Islington, North London, Kemp originally started out attending theater clubs alongside his brother Gary at the age of seven appearing in numerous British TV shows, including Dixon of Dock Green and The Tomorrow People. In the late '70s, Kemp's brother started a new wave band, Gentry, and after a short time, Kemp joined as bassist, with the band renaming themselves Spandau Ballet. Over the next few years, the group became one of the acts that would spearhead the New Romantic movement, alongside A Flock of Seagulls and Duran Duran. Success came with their third album, 1983's True, which peaked at number one on the U.K. albums chart. Three more albums followed before the group called it quits in 1990 among issues over royalty payments.
That same year, Kemp and his brother Gary returned to their first love, acting, earning the parts of the notorious Kray Brothers in Peter Medak's The Krays. The film's success led Kemp to return to the screen for the next two decades, splitting his time between cinema and television. 1998 saw him take on the role of TV bad boy Steve Owen in the long-running British BBC soap opera Eastenders before leaving four years later after his character was killed off in an explosive car chase.
In 2009, Spandau Ballet announced their re-formation, with the group embarking on a nationwide tour as well as releasing a new album, Once More, which saw them reworking their back catalog. While the band continued to tour and play, Kemp also continued with his acting career, appearing in British television drama, hosting documentaries, and acting in stage musicals like 2016's Chitty Chitty Bang Bang.
With original vocalist Tony Hadley quitting Spandau Ballet in 2017, the group once again broke up, officially ending in 2019. After some 30 years of marriage to original Wham! backing vocalist and one-half of Pepsi Shirlie, Kemp returned to the studio with his wife, Shirlie, for the first time to record their debut album. Taking on a selection of easy listening standards with the backing of a big band, the pair issued In the Swing of It at the end of the year and embarked on their first tour together. ~ Rich Wilson, Rovi