The main reason for Saki's setting his story at that specific time and even giving the story the title "Dusk" had to do with the fact that the confidence men could not operate safely in broad daylight. The laws against such soliciting must have been much stricter in Saki's time (1870-1916) and more strictly enforced. The streets of London were patrolled on foot by uniformed officers called bobbies who would get to know their beats thoroughly and would recognize shady characters. Naturally the grifters would want to ply their trade in affluent neighborhoods, so these would be the most closely watched.
At the same time, the grifters could not work too late at night because the good citizens would be safe in their homes. Saki devotes some poetic description to dusk, but his main concern was to establish that it was the time when con artists would be most likely to operate. Gortsby would not be lounging on a park bench if it were not relatively early, relatively safe, and still warm.
The fact that nighttime is approaching lends some emotional appeal to the con man's story. It will soon be dark and cold. He won't be able to apply to any social service agency, if there is such an agency, because all offices will be closed. He won't be able to sit up all night in a tavern because he only has a couple of pennies.
The young stranger tells Gortsby:
"In a foreign city I wouldn't mind so much; one could go to one's Consul and get the requisite help from him. Here in one's own land one is far more derelict if one gets into a fix. Unless I can find some decent chap to swallow my story and lend me some money I seem likely to spend the night on the Embankment."
This part of his story, along with his manner of speaking, conveys the idea that he is an affluent gentleman accustomed to foreign travel and staying in good hotels. He mentions that he had planned to stay at the Patagonian Hotel in Berkshire Square, presumably a prestigious location which English readers of the time would recognize. This makes Gortsby feel safe in lending him a guinea.
"Here is my card with my address," continued Gortsby; "any day this week will do for returning the money, and here is the soap - don't lose it again it's been a good friend to you."
It seems possible that both the elderly gentleman and the young man were working the same scam. Both could be con artists. The older man may have had more experience with telling the same sob story and had actually procured a cake of soap and dropped it under the bench on leaving, with the intention of coming back to retrieve it and using it as an excuse to start a conversation with Gortsby. There would be nothing unusual about two men using the same swindle. We often hear the same stories from panhandlers in America today; e.g., "I need fifty cents to make a phone call." "I ran out of gas and I just need enough to buy one gallon."
In fact, the young man could have been a protege of the elderly gentleman. In Jim Thompson's hard-boiled novel The Grifters (made into an excellent movie with the same title in 1990), the author tells how practitioners of the "short con" learned their craft from older men who were legendary. If the two who talked to Gortsby in the dusk were both con men, it was just a coincidence that both approached Gortsby in the dusk at slightly different times because he looked like a good mark--which he was.