Hmmm can't agree with most of this
Yes it varies by area but you could say the same about anywhere else - the culture of Tower hamlets is going to be pretty different to the culture of Oxford or Brighton.
You could break "different lifestyles and experinces" down to different neighbourhoods only streets away from each other in pontcanna vs Riverside but that wasn't what the op was asking - they were talking on a national level/ the countries as wholes and it is undisputable fact- there are NO grammar schools in the whole of Wales and, while YOU might know a number of people who went/go to private school but statistically,, in the country as a whole, that's unusual - according to This there are only 19 private schools in the whole of Wales- and those are concentrated in certain areas (mainly Monmouth and cardiff) so there are whole counties in Wales without any private schools at all. The same article says that 5 counties in Wales didn't have any children educated privately.
So instead of 7-10% of kids going to private school and another 10-15% going to grammar, 99-100% of kids in many many areas will go to the local state school regardless of their family background. That is going to have a huge impact on the way people interact and grow up.
As for the rest - that's your experience -I can only report my own and say that, despite of course understanding growing up that some families were richer/poorer than others and some parents did different jobs, I didn't have anything like the concept of defined social "class" that ALL the new English friends/acquaintances I met at uni seemed to have an inherent understanding of, and even now that I "get" it, it's not something that figures in my daily life or I ever discuss and think about - whereas the extent to which the topic is discussed on here (not to mention all the newspaper articles, books etc) on it suggests there are a lot of people in England who are still very interested in it.
Just one example -it's weird to me that riding/keeping horses is seen as a middle or upper class activity when every single person I know who rides regularly is very much not posh or well off at all, just live in the countryside!