In Britain it starts well before University, when the scions of the elites attend very exclusive "Public Schools" as teenagers (in typical British fashion, "Public" here doesn't mean state-sponsored like everywhere else, it means private and "open to anybody who can afford it" and even that last part is a lie for the most exclusive ones).
Mind you, whilst I wrote my previous post I kept going back and correcting things because the more I thought about the US in this context the more it seemed to me that the US nowadays does have a lot of that, it's just not as old and entrenched as in Britain plus the mindset of most people there isn't one of "people should know their place" as is in the UK.
I supposed you could say that whilst both countries are not at all meritocratic, people in the UK accept it as "the way things are" whilst people in the US still now (though it seems to be changing) deceive themselves into thinking "one day that might be me".