TEESSIDE, England — As an aging train pulls into view, two men wait patiently in the biting cold, taking photos as the diesel-driven carriages grind slowly to a halt, before jumping quickly aboard.

It is not a good idea to miss the 2:56 p.m. service to Darlington: The next train will call here in precisely one week.

At England’s least popular railway station, here in Teesside, the only travelers these days are those attracted by the novelty and rarity of their journey, which lasts a maximum of 14 minutes.

“The more obscure it is, the more interesting it is for rail enthusiasts,” said one of the men, Henry Kennedy, from Southampton. Along with Murray Colpman, he had traveled hundreds of miles by train, then walked for 45 minutes, to reach this obscure transportation outpost in northeastern England.