He soon moved on to Winsford United, who he played for until Bolton Wanderers gave him his first Football League chance when they signed him in April 1984.
But a broken leg early in the 1988–89 season after a tackle by Chester City's striker Ian Benjamin ruled him out for more than a year thus ending interest in him by Arsenal, Ipswich Town and Everton.
The campaign memorably saw him deputise in goal for nearly the entire 90 minutes away at Scarborough after regular goalkeeper Billy Stewart suffered an injury in the warm-up.
Came kept a clean sheet as Chester won 1–0 and he struck up a solid central defensive pairing with Colin Greenall as City sealed the runners-up spot.
But in July 1994 Came opted to remain in Division Three by joining Exeter City, where he won player of the season in his two years with the Grecians.