In the novel Five Little Pigs, Gillespie Buildings is a residential building in London. After leaving her employment with the Crale family, Miss Williams moved into flat no. 584.
The Gillespie is described as "a bare building" and no. 584 is on the top floor. Judging by the kind of flat Miss Williams had, the building is very downmarket. Her flat only has one room serving as bedroom, sitting room, dining room and kitchen (with a single gas ring). A small cubicle served as the bathroom. It was, Poirot reflected, the kind of dwelling for the "little pig who had none."