Beasley began his professional career with Birmingham, but left to join Torquay United in 1935 without making the first team He played in the following two games, a 2–0 defeat away to Bristol City and a 3–1 defeat at home to Millwall in which Beasley scored Torquay"s goal. Despite scoring he was replaced by Wally Hunt for the next game.
He made one further appearance, on 14 April 1936 in a 3–0 defeat away to Bristol Rovers, before leaving for non-league Worcester City, for whom he scored 43 goals in league and cup.
He later played for Halesowen Town.