Outside-right Watkinson was described by LFC's handbook in 1949 as "a strong type of player, possessing a good shot." William was a local player (born in Prescot) who played for the club 24 times in the period immediately following the end of the Second World War. Liverpool won the first post-war championship in 1946-47 and William played in the last six matches of that memorable and seemingly-endless season, scoring on his debut at Aston Villa on 26th April 1947 and also being in the side for the 'title decider' at Wolverhampton on the last day of May (although the players had an agonising wait of several days into June before other results meant that they could not be caught).
Although he played in the first seven league games the following season before losing his place to Bob Priday, it was always going to be hard to keep a spot in a forward-line with the experience and goal-scoring abilities of men like Liddell, Stubbins & Balmer. He made the line-up for the first six matches of the 1948-49 season, but then lost his place to Jimmy Payne. William's final appearance for the club came at Portsmouth on April 22, 1950. He was transferred to Accrington Stanley in January 1951 for a club record fee of approximately £3,000. He scored an impressive 45 times in 105 league matches for Stanley, and later had a spell with Halifax where he scored 24 goals in 60 appearances in the league.