The opening clues us in that "Shot in the Dark" was written and set in the past, for in this story, trains appear to be the normal way to travel. If the story were set in our time, it's much more likely that Philip Sletherby would drive down to the country estate in question.
Reinforcing the fact that most people travel by train, Sletherby runs into a club acquaintance on the train platform. Further, while on the train, Sletherby shares a compartment with a traveling companion who claims to be his hostess's second son, Bertie. As his hostess is socially important, and as Sletherby and his friend belong to a club, indicating they are also in the middle or upper class, we know that even well-to-do people travel by train. This would be far more typical of the world of a century ago than today.
Finally, Bertie asks to borrow three pounds to pay for his weekend trip—today you would need far more money than that for even a very modest weekend vacation.