Yes, as I understand it the universities retain some semblance of authority because they are awarding the degree.
The school I was talking about was a "valued partner" school (with my university).
I love my job (primary) - I have toyed with teaching English to secondary school pupils, but I just can't stand the idea of teaching 30 13 year olds, the vast majority of whom do not want to be there. I have so much respect for secondary school teachers, particularly in less popular subjects, but I just can't see any solution to encourage more people into it (short of offering vast amounts of money, which isn't practical and might not attract the right candidates).