The Avenger by Edward Phillips Oppenheim

Herbert Wrayson, a bachelor returns to his flat one night to find a young lady rifling his desk. He questions her and finds she thought she was in the apartment of his neighbor, Morris Barnes, who lives above him. While he is on the telephone, she quietly slips out of his flat and heads to Barnes’ abode. A few hours later, she is once again at his door – this time looking scared and faint. She asks Wrayson to escort her downstairs as the hallway is unlit. As they emerge, a hansom sits at the doorway