An old bastile-house (Hebburn Castle or Tower, the old seat of the family of Hebburn) stands in the southern part of Chillingham Park, from which a concealed passage was said to have passed to a pillar-like stone, named the Horl-stone or Hurl-stone, in a field near the New Town of Chillingham or Chillingham Newton.
Hebburn Castle must be Hepburn Bastle, a 16th century tower house in Chillingham Park, which is a mile or two to the east, across the river.
Horl-stone is by some conjectured to be Earl’s Stone. It was erected in a socket by Mr. Jobson, late farmer of Chillingham Newton: and some years ago had a portion struck off it by lightning.
These quotes are from the Denham tracts, and you can read more from them about the connection between the Hurlstone and Cateran’s Hole on the latter’s page.