I agree that it's silly to pretend class distinctions don't exist. But how the hell do you define them? You can do it by income, I guess. But that isn't really the same as 'having class'. I know several rich people, for example, who are ignorant, loud, vulgar and repellent. They have plenty of money, but no class. And I know other people who live in social housing yet have post-graduate degrees.
I've never connected social class with money. For me, your class is determined by:
Your level of education
Your reading habits
Your taste (in art, books, fashion, jokes, etc)
Your way of speaking (by which I don't mean an RP accent, I just mean pleasant, sensible and articulate)
Your manners/how you conduct yourself/how you interact with others
Of the traits I've listed, how you conduct yourself/interact with others is the most important. Some people just have no idea how to behave. They are incapable of holding a civilized conversation. Instead, they talk over you, assert things aggressively, beat you down on every point, avoid eye contact, and so on.
For example, I belong to a book group. The people who attend are all polite, intelligent, and well-read. None of them are rich, none of them went to private schools, and none of them are 'posh'. In fact, a couple of them live in social housing. But they know how to behave. They smile, ask how your weekend was, make self-effacing jokes, listen when you speak, disagree in a calm and non-threatening manner, etc. I can think of several very rich people, however, who wouldn't fit into that group. They are too loud and brash and common (and pretentious). They wouldn't be comfortable because they wouldn't know how to behave.