A wayleave is a legal agreement which allows somebody to enter or cross someone else's land or property for a particular purpose - today used by utility companies to maintain our water supplies, sewers, power supplies, communications, etc.
From about 1600 wayleaves were commonly used in NE England to allow coal to be moved from pit to port. They could be highly restrictive, withheld, not renewed & short term. Charges could be increased due to changing business associations - making particular collieries uneconomical, forcing sales of leases & pits. An old Pont Valley article gives more background.
In the 1720s the Tanfield Waggonway was set up by owners of land & collieries (the Grand Allies) as part of a 99 year binding legal agreement encompassing coal production & use of the waggonway & staiths. This gave investment stability covering nearly half the coal destined for SE England, & meant that supply & prices could be controlled. See Tomlinson p7-10 for details.
The Brandling Junction Railway transported coal on the Tanfield route in the 1830s, the NER did likewise from 1865, followed by the LNER in 1923, each company operating using wayleaves. The operator of the route was nationalized in 1948, but BR continued using wayleaves. Thus the Tanfield Branch was never owned by a railway company, only operated by them (like Britain's railways today).
"The Tanfield branch was a way-leave line, the greater portion of which was formed through the estate of Lord Ravensworth." - Tomlinson p330. Only the foot of the branch between Redheugh gasworks & Redheugh junction was owned by the NER.