Drummy, who played as a midfielder, began his career with the youth team at Arsenal. He never made the first team at Arsenal, but did make five appearances in the Football League on loan at Blackpool. He later played non-league football for Hendon, Wealdstone, St Albans City F.C. and Enfield. While at Hendon, Drummy scored in the Final of the 1988 Middlesex Senior Charity Cup. He also played for Ware.
He is currently the international head coach of Chelsea,