I'm not sure what your question is about universities. The price of university in the UK is higher for non-EU citizens, so there is a preference and benefit for EU citizens today. My son, with an EU passport, took advantage of EU membership. If that were not available, we simply would not have gone to the UK, due to the higher barrier of higher costs. There are also many great universities in Europe. My son was looking forward to the international life in London, a city that voted to remain.
I can see how you want to control your sovereignty. But I think that will come at a great cost to Britain and Britains, and you won't realize all of the things you thought Brexit would bring back, because Europe did not take them away.
Coming from the large country of USA, England is little.
I am surrounded by several British nationals who were unable to vote in the democratic referendum. Several of them opted to become EU citizens due to the uncertainty.