The class system in the UK is less linked to money than elsewhere in the world. The two things operate independently of each other, it's more than possible to be incredibly wealthy and working class, or incredibly poor and upper class. The wealth and class are independent though often correlational.

Where race plays into this is once again complicated, because the UK imports a large number of BIPOC into relatively well paid jobs, particularly in the NHS. This creates a problematic class/race situation. Many working class people, often brought up on nostalgic tales of empire consider themselves racially and class superior to people who are theoretically in a much higher wage bracket than they are - and are economically middle class. When you throw in the capacity of different parts of the ex-empire to import their most affluent members here to take advantage of the education system, you get a real complex state of affairs.

If you're genuinely looking for an insight into the UK class system, and it's much more complicated than I'm making it out to be, then I'd recommend a book called 'Watching the English' by Kate Fox, which takes a somewhat idiosynchratic look at this crazy little island and those of us that live here.