Born in Hatfield, Hertfordshire, Dowie was rejected by Southampton aged 16 and later went to the University of Hertfordshire to study for a M.Eng Degree in Engineering. On completion he became an employee of British Aerospace, whilst keeping up football at non-League level playing for Cheshunt alongside his brother Bob. He left Cheshunt to improve his fitness and signed for St Albans City, then moved on to Hendon. While playing for Hendon, Dowie was spotted by Luton Town who signed him in the 1988–89 season, when they were in the First Division. An old-fashioned centre-forward, he then moved in quick succession to Fulham (a brief loan spell), before establishing himself as a first team player in the 1989–90 season when his eight goals in 29 league games helped Luton finish seventeenth.