I have not found the name in the Electoral Roll for 1918 and 1929 so do not know where on the Island this was situated. If any one knows please make a comment below.
Quote from the Benfleet site
Right from the earliest days of our family Father had a summer residence in the district of South East Essex. Because the Duchy of Cornwall was one of Father’s largest customers he named each of these residences in turn The Duchy.