The Further Side of Fear — Helen McCloy

Lydia Grey, an American returning to London after many years, is woken by footsteps in the night. There is someone in her room - of that she is sure. But that is also impossible. There is only one door and it is bolted shut. The windows are eight floors up, and are locked against the winter night.

As the noise recedes she switches on her bedside lamp. No one is there. Was it a dream? An illusion of a half-awakened state? Or is someone out to get her?