Well, you're American so it may be hard for you to understand, but in England there is still a class system in place; it isn't legally enforced or anything but it still exists on a social level. The working class sprung up during the industrial revolution when cottage industries (people working and living off of their own land) were replaced by factories. As a result, the majority of the English population moved from rural areas to very dense urban environments to provide cheap labour for the factories; they were almost always under paid and received no benefits such as health care or disability insurance. It was common for people to die either directly from injuries or because they were crippled in an accident and died on the streets after losing the ability to work (bear in mind that this was in the 17 to 1800s.) My mother's side of the family are all working class; her father was a coal miner who was injured many times due to his profession (lost several fingers and almost an entire arm) and later died of lung cancer due to his work. Both of her brothers worked in factory jobs. She said she had a hard time going through university (she's a pharmacist) because her family were working class, so as you can see it still affects the lives of many people even in modern times (though I must point out that working conditions are infinitely better than what they once were and legally, the class system is no longer practiced.) Although the casualties aren't English, punk lyrics and attitudes in general are of course heavily influenced by the social situation in the UK and the whole "working class" thing is a common theme for both OI! and Punk bands throughout the world.
The way the working class is viewed here has changed drastically over the last century and half, and what was the classic definition of the working class has diminished the almost nothing. And it's funny that you say "we're all working class now" because according to numbers and standards of living, a majority of Americans are poor class. And we can't even necessarily work for a living. Having a massive working class would be a goddamned improvement for us.
Accurately comparing the UK's and US's working class could really only accurately be done by economists and historians from both sides at this. Our economic evolution and history varies and shifts so widely from one another that I don't think the two of us can do it justice on an internet thread.
"Well, you're American so it may be hard for you to understand"
I didn't mean it like that; I was just saying that it is a culural aspect not so well known to Americans which is why I took the time to explain it to him. I wasn't saying Americans were stupid or anything, just that they won't really understand the class system on a personal level because they aren't really affected by it to the same degree.