The league ended when the criminal, John Clay, no longer needed Mr. Wilson away from his shop during the day.
The Red-Headed League was highly unlikely. It was brought to Mr. Wilson’s attention by his assistant, who showed him a newspaper advertisement. The league was supposedly designed to promote red-headed men because an American millionaire named Ezekiah Hopkins had red hair and left the instructions and funding in his will.
In reality, Mr. Wilson had red hair. His shop was near the bank. It was a way to get him out of the shop. When Mr. Wilson hired Sherlock Holmes to find out why the Red-Headed League was disbanded, he figured this out upon visiting the shop. Watson and Holmes discussed this.
Evidently," said I, "Mr. Wilson's assistant counts for a good deal in this mystery of the Red-headed League. I am sure that you inquired your way merely in order that you might see him."
"The knees of his trousers."
Holmes noticed that the man must have been kneeling. He also realized that the man was no assistant, but actually the notorious criminal John Clay. He was using Mr. Wilson’s shop to break into the bank next door by way of making a tunnel. Holmes figured that out and decided that the disbanding of the league meant the robbery was imminent, and therefore he got the bank director to watch with him to prevent it.
"It's no use, John Clay," said Holmes blandly, "you have no chance at all."
"So I see," the other answered, with the utmost coolness. "I fancy that my pal is all right, though I see you have got his coat-tails."
"There are three men waiting for him at the door," said Holmes.
Thus, Holmes took a case that seemed completely silly and solved a bank robbery. Holmes knew that the case was important because the Red-Headed League was so odd. He knew that there had to be something else behind it.