So for instance the story is that Cambridge University was founded by people who were disgruntled at Oxford. Also there's a number of institutions that were founded due to religious affiliation, IIRC UCL in London.

Nowadays there's an entrenchment that makes it hard to just go and do your own uni. It's not illegal, but you need to find supporters who won't just say "hey why don't you just go to X existing uni". And there's already a uni for whatever speciality you're into, plus the big names that are the specialists for every subject.