 In the 1920–21 football season, Cookson made 42 appearances for Manchester City who came second in the league, 5 points behind champions Burnley, which was City's highest position in the league since the 1903–04 football season when City had a team which included Billie Gillespie, Frank Booth and Billy Meredith.The following season, the 1921–22 football season, Billy Meredith returned to Manchester City and played alongside Cookson on the right side of the City team.Cookson made 39 league appearances for Manchester City that season and City finished tenth in the league with 45 points.