"GREEN HAMMERTON, in the parish of Whixley, upper-division of Claro; 7 miles SE. of Boroughbridge and Wetherby, 8 from Knaresborough, 10 from York. Principal Inn, the George, a Posting House. Pop. 329."
"PROVIDENCE GREEN, a single house in the township of Green Hammerton, and parish of Whixley; 7 miles from Knaresborough."
Looking at Google maps, I would say they're about 8 miles apart.