The distances might be right...

...but I have my doubts about the directions.
We arrived at the camp-site, and what a site. It was billiard table flat and the grass looked better than your average front lawn. I think, between us, we saw two patches of 6'' diameter each ... daisies and not another weed in sight.

On the way in I spotted a pole with N.S.E.W. set on top.
On the strength of that I can accept that John o' Groats might be, more or less due North and New York kinda West(ish), but I'm not over sure about Paris being due East or Luxor due South.