“They” being the well-off, yes. Your average working man would hardly ever write one.
The population of greater London in 1900 was over 6 million, which would be the County of London plus the City of London. But the City of London alone only had about 30,000 people living in it at the time.
I don’t know the area covered by the hourly post service mentioned about but I guarantee it would not be the whole city. It would be the City plus the more affluent suburbs around it, I’ll guess something in the region of 100,000 people. It wouldn’t be hard for 100,00 of the richest people in the world at the time to pay for an hourly postal service over a fairly small geographical area.