Drafted in after injuries to first-choice left-halves Albert Cadwell and Joe Musgrave, he made the position his own and rarely missed a game up to the outbreak of World War II.

[3][4] Cockroft played as a left-half, but often switched positions with Len Goulden during matches to dumbfound oppositions.

[3][4][5] Cockroft played in the first three games of the 1939–40 season, but these were expunged from the records after the League was suspended following the outbreak of World War II.

[7] He played for the Owls in the northern final of the War Cup in 1943, and went on to join the club after hostilities ended.

[9] His debut came on 5 January 1946 in a goalless FA Cup 3rd round first leg game against Mansfield Town.