@James there's nothing wrong with drawing the wrong conclusions from research. Even the wrong conclusions can be very helpful in enabling the research to move forward. Your last post gave me a whole new angle on the area. Previously in my research, I've followed the family from Crofton through Cowpen, Bebside, Bebside Furnace, across the river to Walker Road then up to Glebe Road and eventually to Netherton where I was born. Until now I haven't thought about looking at Bebside Furnace area from Bedlington and moving along the riverside as you did in your last post. Now I can see it clearly. As I've moved along the riverside from the furnace area towards Bedlington, the last house on the riverside has always been Rose Cottage - next door to Clock House. Had I gone further, into the next parish I could have been certain that I was correct in my conclusion much earlier. I've been using the census for Cowpen and Bebside which 1891 enumerates "all that part of the township of Cowpen west of the railway (...) and houses along the riverside as far as the Bebside Township boundary". Had I just stepped over the boundary I would have found Toll Cottage. For a while I considered it also as Rose Cottage but thanks to your input I see clearly that it is not, because Toll Cottage lies exactly on the parish boundary but not in the Bebside Parish I've researched.
This first map from 1866 has a lot of damage but it shows the boundary clearly with Toll House (Green) immediately to the left. I've marked Clock house (Blue) and Rose Cottage (Red). All can be seen clearly on the second map from 1897. (same colour marking). Now i'm happy! The location of Rose Cottage is decided!