Night Must Fall by Emlyn William.

Danny has already murdered one woman, and there is little doubt that he will soon murder another - the aged owner of the house.  He gradually insinuates himself into her affections in a skilful manner, for Dan is a dashing young assassin, a completely self-centered psychopath with no feelings and a vast imagination, who is perpetually acting, for his own edifications, the part of the murderer.  Period 1935.