I am perfectly aware of what the planning objections would be and how difficult they would be to overcome,
The planning issue would be a big one. To get a railway built and in operation - even a privately funded one - would need an extensive planning process. It’s reasonable to assume that the local poplace would want some benefit from the disruption caused by the construction of the railway, almost certainly in the form of a passenger service. Ie, to overcome the planning issues, you’d need to build a passenger railway.
