My favourite answer;
Carradale, on Kintyre (my neck of the woods) has it's to closest stations on two different lines.
West Kilbride is 40km across the Firth of Clyde and Arran, just edging out Ardrossan Harbour at 41km. These, while part of the same route, are technically separate branchlines.
Obviously however, these stations are across the sea, the only direct route being the three times weekly ferry from Ardrossan to Campbeltown, with a one way trip of approximately 3.5 hours to either station.
It gets very interesting if you measure the distance to the closest station accessible by road. The nearest station in that sense is Arrochar and Tarbet, a little over 80km in a straight line, and a whopping 138km and 3 hours by road.
I'm not sure anywhere else on mainland Britain could really compete with the Kintyre peninsula for road journey time to the nearest station by straight line distance. From Campbeltown to Ardrossan Harbour on a good day, not taking a ferry, you'd be looking at a 227km road journey, taking over four hours, more likely five, and on the way you'd pass within 1km of no fewer than 16 other stations!