I was going to say that it might not even have been the telegraph as mail was delivered multiple times a day in London at one point. So even letter delivery was pretty quick as long as the distance wasn't too great.

But, in this case, you're right. I searched the text and it was indeed telegrams that were being sent.

The Moonstone stands up pretty well. The Woman in White is pretty good too. I haven't read his other books although I'm told they fall off from those two.