| 5. Round | 03/09/1960 | Sheffield Wednesday | - | West Ham United | 1:0 | ||||
| 6. Round | 05/09/1960 | West Ham United | - | Manchester United | 2:1 | ||||
| 7. Round | 10/09/1960 | Chelsea FC | - | West Ham United | 3:2 | ||||
| 8. Round | 14/09/1960 | Manchester United | - | West Ham United | 6:1 | ||||
| 9. Round | 17/09/1960 | West Ham United | - | Blackpool FC | 3:3 | ||||
| 10. Round | 24/09/1960 | Everton FC | - | West Ham United | 4:1 |
England