Having left school, he worked as a delivery boy for a local butcher and later an assistant to a television repairman before becoming an apprentice bricklayer at the age of 16.
Despite this, Tapscott was regularly granted permission to return to South Wales on match weekends to play for Barry Town.
He started off with a prolific run in the reserves, scoring thirteen goals in fifteen matches in the London Combination League.
[7] An injury sustained while playing for Wales during the 1957–58 season, put Tapscott out of Arsenal's first team, and he then struggled to oust his replacement Vic Groves once he had returned to full fitness.
Tapscott is also the club's record holder for the most goals scored within a game with six netted during a 16–0 win over Knighton Town in the Welsh Cup.
Altogether Tapscott scored 102 goals from a sum of 234 appearances for the club making him Cardiff City's sixth-highest goalscorer of all time.
However, he appeared just 15 times for the club, scoring one goal during a 3–1 win over Bradford City on 7 March 1966, before leaving at the end of the 1965–66 season.
Including his debut, Tapscott played in nine consecutive matches between 1954 and 1956, scoring his first international goal during a 2–1 win over England on 22 October 1955.
Tapscott then went on to write his autobiography that was published in 2004 which he entitled Tappy: From Barry Town to Arsenal, Cardiff City and Beyond.