The youngest of seven children born to Harold and Kate, he attended Buslingthorpe School on Meanwood Road and went on to join the RAF.
From his first marriage he had two daughters Beverley and Tracey and was a well liked Publican running the Anchor Inn Hunslet, The Fox and finally The Burtonstone in York.
[3] Jeff Stevenson played scrum-half for Rugby League XIII while at Leeds in the 8-26 defeat by France on Saturday 22 November 1958 at Knowsley Road, St. Helens.
Stevenson played scrum-half, and was man of the match winning the Lance Todd Trophy in Leeds' 9–7 victory over Barrow in the 1957 Challenge Cup Final during the 1956–57 season at Wembley Stadium, London on 11 May 1957, in front of a crowd of 76,318.
Stevenson played scrum-half in Leeds' 24–20 victory over Wakefield Trinity in the 1958 Yorkshire Cup Final during the 1958–59 season at Odsal Stadium, Bradford on Saturday 25 October 1958, and played scrum-half in Hunslet's 12–2 victory over Hull Kingston Rovers in the 1962 Yorkshire Cup Final during the 1962–63 season at Headingley, Leeds on Saturday 27 October 1962.