In 1960–61 Bridgwater reached the first round of the FA Cup for the first time, and after beating Southern League club Hereford United 3–0, they lost 2–1 at another Southern League club, Oxford United. They repeated the feat the following season, beating Weston-super-Mare 1–0 in a first round replay, before losing 3–0 at home to Third Division Crystal Palace. In 1963–64 another first round appearance resulted in a 3–0 defeat at home to Third Division Luton Town; they were beaten in the same round by Reading in 1971–72. The club went on to win the league in 1980–81. After winning the League Cup the following season, they moved up to the Midland Division of the Southern League. However, after two seasons the club resigned from the league and folded due to financial problems caused by the additional travelling, falling attendances and building works at the social club.