In the short story The Under Dog, Inspector Miller was the Scotland Yard inspector who investigated the murder of Sir Reuben Astwell. He noticed that butler Parsons appeared unhappy and uncomfortable because he was holding back something and insisting that the killer was an outside burglar. Miller managed to break Parsons and extract the truth from him about who he had seen coming out of Sir Reuben's study. With this and other evidence, Miller proceeded to arrest Charles Leverson.
Poirot noted that Miller was a "sharp man", a "weasel" or a "ferret". It is not clear if this Miller is the same person as various other inspector Millers mentioned in other short stories. Here Poirot mentions that he has dealt with Miller "once or twice", suggesting that this is possible.