Fee hike in mid-course

Hey, I'm a prospective medical student for 2016 entry in Imperial college London. This is a 6-year course, and the UK is officially leaving the EU in 2 years or so (at least, that's what it looks like). Is there a possibility that after that, halfway through, for the remaining 4 years of my course, my university fees will suddenly get larger (say, to the level of international fees)? If I suddenly need to pay international fees I won't be able to continue studying, and will need to quit halfway through to go somewhere else, so if that's a possibility I might as well just leave now.
Hope this isn't a stupid question.