After recording Spandau Ballet's final album, Kemp and his brother became actors. He won the contempt of his fellow band members, but good reviews for his performance as Ronnie Kray in The Krays (1991). Making this film was the death-knell to Spandau Ballet.
He was married to actress Sadie Frost with whom he had one son, Finlay Munro (born 1990). The couple divorced in 1997, after she left him for Jude Law. Kemp is now married to costume designer Lauren Barber with whom he now has another son Milo Wolf.
He has also written two productions with Guy Pratt for the stage: "Bedbug" which was performed in a variety of venues during the Shell Connections Youth Drama Festival in 2004; and "A Terrible Beauty" which is based on the life of William Butler Yeats & Maude Gonne. This has yet to find financial backing.