Allen was born in Deiniolen, Gwynedd, but began his career with Watford, signing apprentice terms in July 1983, before becoming professional in March 1985. He scored Watford's only goal in 1985 FA Youth Cup final. He played and scored for the Hornets in their FA Cup semi-final defeat against Tottenham Hotspur in 1987, and in 19 cup appearances for Watford scored eight goals. He was loaned to Aston Villa in September 1987 by new Watford manager Dave Bassett, and after Watford were relegated he joined Norwich for a fee of £175,000 in August 1988. Whilst with Norwich he scored four in their club record FA Cup victory, 8–0 against Sutton United in the fourth round. This was one of the most successful seasons in Norwich's history, as they finished fourth in the league and were semi-finalists in the FA Cup.