Having spent a couple of days in Kirkby Stephen this summer, I recognised the square straight away. The disused line is the old Tebay-Darlington line that goes across Stainmore.
I can recommend spending some time in the area, the Northern Viaduct Trust has done a great job in preserving the old viaducts on the disused line and there are excellent footpaths across them. The site of the Belah viaduct can be accessed too (the abutments and carcass of the old signal box remain). Also, the preservation society at Kirkby Stephen East station are a very friendly bunch and I was much surprised to (a) see that the old station has survived and (b) to see an ex-Barry wreck of a 9F there.