A product of the youth team, Minton scored one goal on his debut against Everton in a 3-3 draw and starred in one more match in 1992 before the midfielder left in 1994 for Brighton and Hove Albion.
Jeff was a darting forward, who scored and set up goals for the Spurs youth and reserve teams before he got his chance in Gazza and Gary Lineker's last home game for Tottenham. He almost stole the show, as he scored a good goal on the turn, although this proved to be only one of his two showings in a Spurs first team shirt. Failing to break through again, he moved on to Brighton and spent five years with the Seagulls, before he signed for Port Vale in July 1999, where he scored four times in 36 league games for the Midlands side.
In March 2001, Jeff moved on to Rotherham United before he returned to London with Leyton Orient in the close season before the 2001-2002 season. Despite being offered a two year deal with The O's, Jeff moved to Grays Athletic in 2002, but it was a short stay of only two weeks before he was tempted to join non-league side Canvey Island and then Chelmsford City, signed by his former manager at Canvey Jeff King, where he helped them climb back to the Blue Square Southern Conference as champions of the Rymans League in 2007-08.
Released in June 2009, he moved to Welling United a month later, where he became captain, but only lasted for a month before being allowed to leave.