Some unbelievably anal research to get what I'm fairly confident is the right answer:
10. Cilmeri Station. Heart of Wales Line.
That research included looking for examples of 39^ miles in the National Rail Timetable and 39 miles 40 chains in the Sectional Appendices. Drew a blank. Then looking at random stations to see which
TOC▸ painted their lamposts that way. Then noticing the dark cyan band on the station name board behind the overhanging tree. Those last two colour clues led me to the conclusion it was an Arriva Trains Wales station. Then thinking this must be railtour because of the glimpse of carriage and the window hanging. Then pondering, where might a railtour go through small country stations in Wales? So I plumped for the Heart of Wales Line and went back to the mileage. Cilmeri station is 39^ miles from the junction at Craven Arms. Finally, looking at some images of Cilmeri station online to confirm features.
Bingo!
Can I go to bed now?!
(And may I just say, I compiled this post and posted it without reading Phil's additional clues at 11:32pm. Yes, I really was working on the answer for over an hour. I'd've been gutted if someone had popped up and got the right answer. Thank cripes it wasn't Taunton!)