I think you should check out the regulations, Mair.
EU nationals are only eligible for 'home status' (ie to be treated as 'our own'), be eligible for UK fees and be able to apply for a loan, if they have been settled in the UK for at least three years before the start of the course. They also have to meet language ability criteria. It is cheaper to study in their country of origin.
The EU is actually advantageous for UK students, because they can apply for courses in EU universities and only have to pay local fees, which are much cheaper than UK universities. Although they have to meet language criteria for some courses, some universities are now running courses in English.
UK universities stand to lose financially from leaving the UK, because many EU and international students are self-funded and pay much higher fees than home students. Some also bring research grants with them from their country of origin. These are in addition to the number of UK students which the British government is willing to fund. Losing them will not mean that there are places available for UK students. There has already been a decrease in the number of EU and international students applying for British universities, so the universities will lose financially.