A Great Britain international representative three-quarter back, he played club level rugby league (RL) for Warrington (with whom he won the 1954 Challenge Cup), and Barrow (who he also captained).

[9] Challinor had been offered a trial at Manchester United, but made his début aged-18 for Warrington against St. Helens in October 1952, he initially played on the wing, but later moved into the centres.

Challinor played right-centre and scored the first try in Warrington's 8–4 victory over Halifax in the 1953–54 Challenge Cup Final replay during the 1953–54 season at Odsal Stadium, Bradford on Wednesday 5 May 1954, in front of a record crowd of 102,575 or more.

Challinor played in the 5–4 victory over St. Helens in the 1959–60 Lancashire Cup Final during the 1959–60 season at Central Park, Wigan on Saturday 31 October 1959, in front of a crowd of 39,237.

He played right-centre and was captain-coach in Barrow's 12–17 defeat by Featherstone Rovers in the 1966–67 Challenge Cup Final during the 1966–67 season at Wembley Stadium, London on Saturday 13 May 1967.

Challinor coached St Helens to the 16–12 victory over Wigan in the 1970–71 season's Championship Final at Station Road, Swinton on Saturday 22 May 1971.