Walton & Hersham were elected to the Isthmian League in 1971, and the 1972–73 season proved statistically their greatest ever. They won the Surrey Senior Cup, finished as runners-up in the league, reached the FA Cup Second Round for the first time and, most prestigiously, won the FA Amateur Cup, defeating Slough Town at Wembley Stadium. They set a unique record by winning the competition without conceding a goal. Players including Dave Bassett, Willie Smith and Roger Connell became regulars in the England amateur international team. As FA Amateur Cup Winners they were invited to compete in the 1973 Final of The Coppa Ottorino Barassi (The Barassi Cup). They played Jesolo the Italian Amamtuer Cup Winners. The Swans won both legs 4-0 at home and 2-0 Away to lift the trophy. In 1973–74, the club reached the FA Cup Second Round again, having beaten Brian Clough's Brighton & Hove Albion at Goldstone Ground 4–0. Following the defeat, Clough almost got into a fight with comedian Eric Sykes, who was associated with Brighton & Hove Albion at the time and was laughing about the result to a friend during a phone call.