Shrubb began his career in the youth system at Second Division club Fulham and signed his first professional contract in 1972.
[6] The high point of his time with the club was reaching the final of the 1976 NFL Cup, which was lost to Cape Town City.
[9] He made 202 appearances and scored six goals during a five-season spell and departed after the Shots' success in the 1987 Fourth Division play-off final.
[10][11] He put his skills as a utility player to good use, wearing every single shirt number (1–11) during his time with the club.
[9][13] Shrubb was awarded a testimonial versus Charlton Athletic on 1 August 2007, in recognition of his service to the club.
[15] After his retirement from playing, Shrubb served as Steve Wigley's assistant, before departing the Recreation Ground for the final time in 1997.