Chelsea 6-0 West Ham United (1956-57 SEC League Cup)
From TheChels.info - The Chelsea Football Club Wiki
|  13 April 1957  | CHELSEA | 6 - 0 | WEST HAM UNITED |  Venue: Stamford Bridge, London Attendance: n/a Referee: Mr. E Bolton  | 
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|    Block     Clarkson Cliss Abrey  | 
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Notes
Remarkably West Ham United played 2 youth games on the same day, 
 with 5 players appearing in both games!