At my institution, we are looking at what happened to the Swiss in participating in various educational & research schemes with the EU. The deal hinged on the Swiss reluctance to allow freedom of movement; the EU does not budge on that (thank goodness!) The EU prevailed.
Brexiteers are very gung ho about controlling borders, immigration, and getting rid of EU freedom of movement principles. So it is highly unlikely once Article 50 is passed, that the EU will remain open to UK citizens in the way it is now. The next generation's loss.
So those advising on this thread about caution are absolutely correct. In academia, we are watching what's happened elsewhere, and making quite logical, evidence-based inferences from it.
The other things to think about in terms of a university education elsewhere in Europe are about language, culture, what sort of university experience you/your DC want, and what they want to do after graduation.
If your DC want a career principally in the UK, then do a degree in the UK, but one which has the possibility of a year/semester abroad.
If you're looking at the rest of Europe (including the EU) for reasons of saving money on fees, that is the wrong criterion. It's a false economy, and probably not that much of an economy.