1000% I've now moved to the US and the difference is stark.
I remember when I landed my first job at a big company in London how many people tried to guess which school I went to or referred to how certain people came from "good" families. I was, and still am, the only British person in my team who didn't go to a private school. My boss was fascinated by how frugal I was, probably because everyone she'd previously hired had a trust fund or a flat bought for them!
It's not like America doesn't have a class system but it doesn't have the same hereditary/exclusionary culture around it. In the US you're upper class if you make enough money, and there are still barriers to that but they aren't enshrined in the culture in the same way. Although the US has the additional dynamic of race which is much worse in some ways.