This is Towerhirst, on Sea Walls Road, "A fine example of domestic architecture in the Free Gothic style", according to the listing. I heard somewhere that it was a wine merchant's house, and that he had the tower built so he could watch for his ships coming in, but I can't find much to back up that story. Apparently built c. 1891.
GPS Coordinates:
51.46972, -2.63246
Location: Sneyd Park and the Downs