He started his career at Crystal Palace, before spending eleven years with Watford. He played for the club whilst they were both bottom and top of The Football League. Jenkins became an apprentice at Crystal Palace in July 1968, signing professional terms in November 1969.
In November 1972 he was bought by Watford manager George Kirby for a then club-record fee of £30,000 initially, with £5000 to come a year later.
Kirby had made a series of unsuccessful bids for other players before signing Jenkins. The following season, under new manager Mike Keen, Jenkins only scored four goals in 26 appearances.
Watford were relegated from the Third Division in 1974-1975 season, with Jenkins finishing top scorer with 11 goals in 34 appearances. In the summer of 1975 Jenkins chose to turn down a transfer to Huddersfield Town for a fee of £12,000.
After a 1–0 defeat to Darlington, which Jenkins played in, their fourth game and defeat of the 1975-1976 season Watford were bottom of the Fourth Division.
The club had a strong second half of the season and finished eighth, with Jenkins top-scorer with 19 goals. In summer 1977 Keen was sacked and Graham Taylor was brought in. Under Taylor Watford advanced through the leagues, with Jenkins in the side.
They were promoted from the Fourth Division in 1977-1978, the Third in 1978-1979 and the Second in 1981-1982.
They eventually finished second to Liverpool and Jenkins left Watford at the end of the season to play in Hong Kong. In 1987, Jenkins briefly returned to Watford as a coach, under Dave Bassett"s management.
Jenkins is no relation to the player of the same name who played for Watford between 2008 and 2014.