 Kemp began his career with Harrow Borough, subsequently playing for Maidenhead United and Slough Town before joining Crystal Palace in April 1975.He moved to Portsmouth in November 1976 and was their leading goalscorer in both the 1976–77 and 1977–78 seasons, despite not playing a full season for the club.A hugely popular player whilst at the club he even featured in Roy of the Rovers magazine photographed alongside his fictional goalscoring counterpart.