[2][3] Starting his career in rugby union, he played for the Cardiff club and after being capped for Wales in 1971, Bevan toured Australia and New Zealand with the British Lions.
In September 1973, Bevan switched to rugby league, and joined Warrington for the then massive signing on fee of £12,000 (based on increases in average earnings, this would be approximately £200,000 in 2015).
[4] John Bevan played left wing in Warrington's 24–9 victory over Featherstone Rovers in the 1974 Challenge Cup Final during the 1973–74 season at Wembley Stadium, London on Saturday 11 May 1974, in front of a crowd of 77,400, and played left wing, and scored a try in the 7–14 defeat by Widnes in the 1975 Challenge Cup Final during the 1974–75 season at Wembley Stadium, London on Saturday 10 May 1975, in front of a crowd of 85,998.
John Bevan played left-centre and scored a try in Warrington's 26–10 victory over Wigan in the 1980 Lancashire Cup Final during the 1980–81 season at Knowsley Road, St. Helens, on Saturday 4 October 1980, played left-centre in the 16–0 victory over St. Helens in the 1982 Lancashire Cup Final during the 1982–83 season at Central Park, Wigan on Saturday 23 October 1982.
John Bevan played left wing and scored a try in Warrington's 27–16 victory over Rochdale Hornets in the 1973–74 Player's No.6 Trophy Final during the 1973–74 season at Central Park, Wigan on Saturday 9 February 1974, played left wing, and scored a try in the 9–4 victory over Widnes in the 1977–78 John Player Trophy Final during the 1977–78 season at Knowsley Road, St. Helens on Saturday 28 January 1978, and played left-centre and scored 2-tries in the 12–5 victory over Barrow in the 1980–81 John Player Trophy Final during the 1977–78 season at Knowsley Road, St. Helens on Saturday 24 January 1981.
John Bevan played left wing in Warrington's 4–0 victory over Featherstone Rovers in the 1973–74 Captain Morgan Trophy Final during the 1973–74 season at The Willows, Salford on Saturday 26 January 1974, in front of a crowd of 5,259.