Quixall signed with Sheffield Wednesday as an amateur in 1948 and turned professional in 1950. He made his debut in February 1951 as a 17-year-old centre forward and went on to play almost 250 League games, scoring 66 League and Cup goals with the Owls. He was in his prime with Sheffield Wednesday, and gained much media attention, becoming the "Golden Boy" of British football.[3] He helped the club win promotion in 1952 and 1956 and appeared in the 1954 FA-Cup semi-final.[2]
Quixall joined Manchester United in September 1958 for a then British record fee of £45,000, one of Matt Busby's key recruits in building a new team in the aftermath of the Munich air disaster, which had killed eight players and ended the careers of two others on 6 February that year.[4] After seven games without a win for United, Quixall eventually helped the team go on a run of only two losses in 23 matches to end the season as runners-up in the First Division.[3]
Quixall's only medal with the club was the 1963 FA Cup. Altogether, he scored 56 goals in 184 games for the Red Devils.[5] Manchester United midfielder Bobby Charlton recalled in his autobiography that Quixall played a key role in many of his goals in this era. He noted that Quixall "played a significant role in my rush of goals. When I broke through an offside trap, often it was to get on to the end of one of Albert's perfectly placed passes".[6]
Along with Johnny Giles and David Herd, he was dropped after Everton beat United 4–0 in the 1963 FA Charity Shield. He rarely featured in the 1963–64 season, last appearing for United on Boxing Day 1963.[7] He left the club at the end of the season, moving to Oldham Athletic for £7,000, spending two years at Boundary Park before finishing his professional career at Stockport County in 1967.[3] Quixall afterwards spent brief spells at non-league Altrincham and Radcliffe Borough.[8]