I would suggest that HMG will take an entirely pragmatic view, and encourage such 'foreign' trade.
Appropriate student training visas will be issued and I suspect with practical transitions arrangements with the rest of the EU.
I don't think bona fide UK ATOs will have any difficultly at all.
The issue has been the "control" of Brussels, not the single market per se.
As to how EU airlines will operate, that is an entirely different matter.
Remember to reread this towards the end of 2018, and see whether it was correct or a complete load of old
