| 16. Round | 07/11/1959 | West Ham United | - | Manchester City | 4:1 |  |
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| 17. Round | 14/11/1959 | Arsenal FC | - | West Ham United | 1:3 | |
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| 18. Round | 21/11/1959 | West Ham United | - | Wolverhampton Wanderers | 3:2 | ||||
| 19. Round | 28/11/1959 | Sheffield Wednesday | - | West Ham United | 7:0 | ||||
| 20. Round | 05/12/1959 | West Ham United | - | Nottingham Forest | 4:1 | |
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| 21. Round | 12/12/1959 | Blackburn Rovers | - | West Ham United | 6:2 | ||||
| 22. Round | 19/12/1959 | Leicester City | - | West Ham United | 2:1 | |
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| 25. Round | 02/01/1960 | West Ham United | - | Burnley FC | 2:5 | ||||
| 26. Round | 16/01/1960 | Leeds United | - | West Ham United | 3:0 |
England