Born in Rotherham, South Yorkshire, England, Dungworth began his playing career at Huddersfield Town, where he signed schoolboy forms in 1969, and scored on his first-team début against Middlesbrough in 1972. He was then transferred to Oldham Athletic in 1975 followed by a successful spell at Aldershot, where he scored 66 goals in 118 games. In 1977/78 he hit 23 goals in 45 league games and was voted Supporters Player of the Year. The following season John was ever present scoring 26 times to break the all time Shots record for league goals in a season. However some of his best performances in 1978/79 were in the F.A. Cup where Aldershot lost in a 5th Round Replay, with John scoring 8 times in the clubs cup run to make him the second highest scorer in the country with 34 goals. He picked up the Adidas Golden Boot Award for being the leading marksman in the 4th Division. He joined Shrewsbury Town in October 1979, a Football League Tribunal setting the fee at £100,000, where he never hit the heights of his past scoring records. Later John moved into the back four and ended his career as a centre-half at his home town club Rotherham United.
Since he ended his playing career, he has been a coach at Sheffield United and manager of Leeds United's academy. Subsequently he rejoined Huddersfield Town, initially as reserve team coach, and then being appointed First Team Coach in December 2006, when Terry Yorath resigned due to ill health. He left on 3 April 2008, announced as by 'mutual consent', following the departure of manager Andy Ritchie two days earlier. He joined Sheffield Wednesday in early 2009 with primary responsibility for coaching the reserve team, but departed in December 2009 along with manager Brian Laws.