Tbh I think EU students should be treated as international students just like people from India, Australia, Nigeria and anywhere else outside the EU. Anyway, in answer to the question, even if fee status does change (which I don't think it will), leaving the EU will take at least 2 years, so the very earliest that people could be affected if EU students become intl. students is people joining uni around 2018/19.
I am an Oxford offer holder and have got 2 emails since Brexit saying how EU students will not be affected and how we need to wait before the UK comes up with a deal with Europe before we know about fee changes