After a look at old OS map imagery, this looks like an old colliery line - possibly narrow gauge?
Scremerston Colliery is shown as disused in 1937-61 editions with a footpath here (walk to work?). OS War Office maps show Scremerston Colliery (Restoration Pit) to the North, and Scremerston Old Colliery, but no railway.
Footpath 203/022 and 203/022 bend here - is the bridge passable?
Sadly, imagery only shows the trees so ground survey is needed. 