| 34. Round | 21/03/1959 | West Ham United | - | Bolton Wanderers | 4:3 |  |
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| 35. Round | 27/03/1959 | West Ham United | - | Newcastle United | 3:0 | |
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| 36. Round | 28/03/1959 | Arsenal FC | - | West Ham United | 1:2 | ||||
| 37. Round | 30/03/1959 | Newcastle United | - | West Ham United | 3:1 | |
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| 38. Round | 04/04/1959 | West Ham United | - | Everton FC | 3:2 | ||||
| 26. Round | 13/04/1959 | West Ham United | - | Luton Town | 0:0 |
England