He made his debut on 11 November 1972 in a 1–1 draw at home to Huddersfield, but was injured on his debut, and was not selected by new manager Les Allen when he returned to fitness. He didn't really feature for most of the 1972–73 season, making just 14 full and 2 substitute appearances. The following season was more productive for Jenkins, making 36 league and 5 cup appearances, but Swindon were relegated to Division Three. In January 1974, he scored his best goal for the club in an FA Cup third round match away to Portsmouth, when after just four minutes he broke down the left-wing, beat two defenders before firing home a right foot shot from the edge of the area. Swindon drew this match 3–3 but were beaten in the replay.