Your OP is very brief - you don't explain in detail in what way you are seeing or experiencing class-discrimination. Are you talking about inequality of wealth or opportunity, or people's accents etc? I do agree that class consciousness is a thing in every human society. It's absolutely NOT just a British thing, as some people are fond of asserting.
I'm class-conscious - I'm aware that people speak differently, have different attitudes to things, different life experiences - especially in education - but I don't think I'm a snob. I don't judge people favourably or unfavourably because of their social background.. I'm not a social snob - I come from a working class background myself. But I do shun people who are 'ignorant and proud of it' - but you find those in all walks of life.
Education used to be the key to social mobility in this country but it's been less effective in the last few decades. I think that's because of the demise of grammar schools, which, while they had some disadvantages, helped so many working class children to get to university and into professional careers. The well-off middle classes (and there a plenty who aren't well off!) have fled to private schools whereas they once would have been happy with a grammar school. This point of view is very unpopular because inclusivity is now seen as more important than pretty much everything else, but I think it's the 'elephant in the room' when the question about the fall in social mobility comes up.
The other factor (from an educational pov) is the widening of access to university education. I went on a full grant, when only 10% of youngsters went to university. You can't have grants when 50% are expected to go, and so much has resulted from that: dud courses, cynically run by universities, which offer youngsters very little chance of real employment opportunities; more graduates than the market can use, leading to all kinds of shenanigans in recruitment - particularly the importance of 'internships' which the middle classes, and especially those around London, are best able to arrange for their children - and much more! So for many young people, the promise of a university degree hasn't been the door to high earning potential and social mobility that they might have hoped.