At Fulham, playing alongside Andy Ducat and Frank Penn, he was top scorer in 1922–23 accounting for 10 of the team's 43 league goals, in what was generally a low-scoring season in Division Two.
He made a slow start to his Tottenham career, scoring only once in his first season and a half, although he was again selected for England against Belgium on 8 December 1924 (won 4–0).
In 1925–26 however, playing alongside Jimmy Dimmock and Jack Elkes, he struck a rich vein of form scoring three hat tricks in the space of two weeks in October/November 1925,[2] finishing the season as the club's top scorer on 25 goals.
[4] At this stage Osborne contemplated retirement, but remained at The Dell for a further season before returning to London in 1933 to work as a sales representative for Fulham chairman John Dean's company in Putney.
In March 1935, he was invited to join Fulham's board of directors, after special dispensation from the Football Association, thus beginning an involvement with the club that would continue, in various roles, right up to his death over fifty years later.
Intensely superstitious and fond of practising his golf swing in his Cottage office, he steered Fulham to the Second Division title in his first season, with the assistance of team manager Eddie Perry.