-- Alan Kay, some anecdote I forget how to locate
In the US I don't think they hardly reference the trivium or quadrivium, but the structure is loosely based on the principle, so because they have lost the reasoning behind it their course load is much more wild and varied, and sometimes unnecessary.
This is also my main beef with those who claim we should just do vocational training or very narrow course loads... the benefit of wide but shallow knowledge is large when applied properly. The US just doesn't apply it very properly. One thing the US does do much better, I must say, is the egalitarian culture though, which offers people the opportunity to laterally move in education much more freely.
Because of the nine originally-charity schools investigated by the Clarendon Commission, they weren't the two that established that they had constitutions guaranteeing their private character which made them immune to the kind of publicly-directed reorganization the other seven were subjected to under the Public Schools Act. That is, they are "public" in the sense that their basic organization was redirected by the State to correct problems found by a government investigation.
For what it's worth, this is a very American approach to college.
You generally wouldn't spend more than 3 years on an undergrad course as a student in the UK - because you tend to spend the vast majority of time on your chosen degree subject. There's maybe room for one or two optional modules in an unrelated field.