In 1950, Robson made his first-team debut for Fulham, recently promoted to the First Division, in a match against Sheffield Wednesday. He came to regard Fulham as "a nice club, a social club...", but "never... a serious, championship-challenging club". Indeed, he and Fulham were relegated from the top-flight in the 1951–52 season, but he made his return to the First Division, four years later, when he signed for Vic Buckingham's West Bromwich Albion in March 1956. The transfer fee of £25,000 was a club record for West Brom at the time.