Playing mainly as an inside forward, Stubbs started out with his local side, Great Wakering Rovers before signing for Southend United.

He scored five goals that season, including a crucial stoppage time equaliser against Chelsea's main rivals Wolverhampton Wanderers at Molineux, paving the way for teammate Roy Bentley's winner a minute later.

[citation needed] Stubbs' later years at Chelsea saw his playing opportunities reduced by the emergence of talented youngsters such as Jimmy Greaves, Peter Brabrook and Ron Tindall.

He made only sixteen appearances in his final two seasons, though he did play for the representative London XI side which competed in the 1955–58 Inter-Cities Fairs Cup.

When Chelsea won the FA Premier League title in 2004–05, Stubbs and his surviving teammates from the 1954–55 title-winning side, such as Roy Bentley, Stan Willemse, Frank Blunstone and Jim Lewis were invited to the trophy presentation.