 Drummond turned pro in 1975.He won the Tooting Bec Cup for the lowest single-round score posted by a British or Irish player at the 1987 Open Championship at Muirfield, carding a 66 in his second round.In 1996, he finished runner-up to Retief Goosen in the inaugural Slaley Hall Northumberland Challenge and third behind Jesper Parnevik and Colin Montgomerie at the Trophée Lancôme, and finished in 42nd place on that year's European Tour Order of Merit.