The 22-year-old clinched the title with a 21-11 victory over Hertfordshire’s Tom Muir of Harpenden.
Puckett reached the final following a narrow 21-20 win against Darren Parkes (St George’s) in the quarters and a last-four victory over Martin Heitzman (Spartan).
Also in Leamington Spa, the Greenhill Men’s double fours also made the quarter-finals of their competition narrowly losing to Essex, who went on to the final.
Greenhill Ladies Ann Chislett and Bridget Hodder qualified to play in the ladies’ singles, and Hodder and Harry Hovenden took part in the mixed pairs.
Greenhill have also won the Dorset County Men’s Championship League with a game to spare.