In America, "middle class" is a humble term for the average family. In Britain, it's a subtly deprecating term for families with a little too much disposable income. How did this come to be?

This question is perhaps developed in a way that people don't like (middle class can be used as a subtly deprecating term for those with too much money, and sometimes is, but often it just means people in the middle), but I would like a good answer to "Why are what British people call working class* people referred to as middle-class in America?"

*I mean people who own a small house and a car, probably didn't go to university, and work in a non-professional job. And probably live in an area with other working-class people, and have a working-class accent. For example, my uncle is a plumber with a white van who owns a small terraced house in Coventry. He didn't go to university. His daughter lives with her fiance and baby in their own house, she didn't go to university either, and works in a hardware shop on the till. My other uncle is a surveyor and his wife is a housewife, they also didn't go to university and live in a terraced house. They seem pretty archetypal working class to me, but my impression is Americans would describe them as middle-class (because they have jobs and houses). In fact, I've never heard Americans use working-class at all? The closest thing I've heard maybe is blue-collar? So why have the two countries' class systems/labels developed in a different way?