Barnsley began his career as a junior at West Bromwich Albion, turning professional in December 1952, with his only league appearance for the Baggies coming in the 1954-1955 season. In June 1957 he moved to Plymouth Argyle, playing 131 league games before moving to Norwich City for a fee of £2,000 in May 1961. Geoff played an instrumental part in Plymouth"s Division Three title winning season of 1959.
One of his only major honours as a player.
After only eight league games for Norwich, he returned to Devon, signing for Torquay United in December 1962 as understudy to Torquay goalkeeper Terry Adlington. Adlington was an ever-present in the 1962-1963 season, Barnsley having to wait until September 1963 for his Torquay debut, a 1–0 victory at home to Rochdale.
He made just six appearances for Torquay and subsequently left for non-league Dudley Town, before retiring as a player. Today, Geoffrey lives in Sedgley, Wolverhampton.