Sure. It's nightmarish what one would have to do to make it otherwise. The big attempts that I mentioned earlier to end this - dismantling the grammar school system and expanding university entrance has had entirely the opposite effect.
I absolutely disagree with you about both dismantling the grammar schools and expanding university entrance. I think both are good ideas. What is bad is that there is insufficient funding of the educational system with still a disproportionate amount of resources being directed at those who don't really need them as much.