Swinbourne began his career at Wath Wanderers, the
Yorkshire-based nursery club of
Wolverhampton Wanderers. He moved south to join Wolves in 1944 and signed as a professional the following year. After proving himself in the reserve ranks, he made his debut on 17 December 1949 in a 1–1 draw with
Fulham. He came to the fore during the
1950–51 season, replacing
Jesse Pye in the attack, and finished as top goalscorer with 22 goals. Injuries waylaid him the following year, but in the next campaign, forming what was described as "a potent dual spearhead" with
Dennis Wilshaw, he was once again the club's leading scorer with 21 goals. His tally of 24 in the
1953–54 season was a career best and helped Wolves capture their first ever league championship. It was Swinbourne himself who scored twice in the final game, a 2–0 victory over
Tottenham Hotspur that confirmed the title. The following season brought another strong return, including
two goals in Wolves' famous floodlit victory over
Honved of Hungary. In 1955 he scored for
England B in a 1–1 draw against their German counterparts: His career was halted when he damaged his knee while hurdling over a posse of cameramen on the pitchside at
Luton Town's
Kenilworth Road ground in November 1955. After trying to return just weeks later, He was forced to undergo surgery on the injury, but was never able to resume his playing career and retired in May 1957. ==Later life==