Davis won the English Under-19 Billiards Championship in 1976. One of his last wins as a snooker amateur was against Tony Meo, another future professional, in the final of the 1978 Pontins Spring Open. He defended his title a year later, defeating future rival Jimmy White 7–4 in the final. Davis applied in 1978 to become a professional and was initially rejected, before being accepted with effect from 17 September 1978, becoming the youngest of the professional players. He made his professional television debut on Pot Black, where he played against Fred Davis. He played in his first World Snooker Championship in 1979, having won two qualifying matches, but lost 11–13 to Dennis Taylor in the first round proper.