The theme of "The Umbrella Man" is the gullible nature of people.
Dahl's story describes how a man is able to manipulate even skeptical people such as the mother of the narrator who, she declares, is a "suspicious person":
My mother's chin was up and she was staring down at him along the full length of her nose. It was a fearsome thing, this frosty nose stare of my mother's. Most people go to pieces when she gives it to them.
But, the perception of an old gentleman--she knows he's a gentleman, she has told her daughter, by his fine shoes--deceives this skeptical woman. This old gentleman who is willing to selling his £ 20 silk umbrella for £ 1, even though it is worth more, claims that he needs the pound for taxi fare home. For, he explains, he has walked farther than he usually does and now is too exhausted to make the walk back on his "silly old legs." Further, he explains that he has left his wallet in his other jacket--"Isn't that the silliest thing to do?"
After he offers to sell his £ 20 umbrella for only a pound, the daughter gives her mother a stern look for considering "taking advantage of a tired old man." So, the mother offers to just give the man cab fare. But the gentleman will not accept such a thing. "I wouldn't dream of it!" he exclaims. He will only take the pound if she agrees to purchase his umbrella. Believing that she is getting an expensive umbrella for such little money, the mother agrees. As the old gentleman moves away, the mother tells her daughter to get out of the rain and join her under the umbrella.
"Aren't we lucky? I've never had a silk umbrella before. I couldn't afford it....He was a gentleman. I was very pleased I was able to help him."
She congratulates herself on being able to judge the character of a person, and she tells her daughter that she has learned a "very good lesson" by seeing how her mother took her time and "summed up" the old gentleman before giving him the pound. By taking this time, "you'll never make mistakes," she tells her daughter.
Just then, however, the daughter sees the "old" gentleman hurrying with his "silly old legs" that are somehow able to move him down the next street. The daughter observes to her mother that the man neither looks tired nor as though he is trying to catch a taxi.
The two woman follow him. When the mother and daughter see him enter a pub, the disgruntled mother watches in embarrassment and dismay as he orders a triple shot of whiskey and pays for it with her one-pound note. After finishing his drink, the "gentleman" goes to the coat rack and pulls down his coat while at the same time taking an umbrella. He departs the pub, heading in another direction, in search of another gullible victim.