My initial though was the Whitby line, not entirely sure why however 
Sampford Courtenay
Great Ayton doesn't fit the clue TB gave.

That's because it wasn't up when I made my guess![]()
Grosmont
Not Gyspy Lane is it?
Somewhere on the Weardale Railway, so Frosterley is my guess.
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No, that's Stanhope!
looks like a terminus,........ Bridlington?
What?