The lodger - Marie Belloc Lowndes

The Buntings are an elderly London couple who have fallen on hard times. They take in a lodger with the strange name of Mr. Sleuth, who pays handsomely for their shabby rooms. He seems to be a perfect gentleman but none the less they begin to suspect that he may be the Jack-the-Ripper-like serial killer known in the press as 'The Avenger'. As the number of murders in the city begins to mount, and Mr. Bunting's teenage daughter from an earlier marriage comes to stay, the couple must decide what to do about the man in their upstairs rooms...