EASA does take third country applications from the UK, however, not from airlines. Just from manufacturers, MROs, maintenance training, CAMO, ATOs and for individual flight simulators as well as AeMC, of which there is only one in the UK as far as i know. It does not cover licenses in itself or airline ops.
Well, as for easyJet, if they did their homework they have to split the company in three (it is already two parts) latest on brexit day, keep all the OE-aircraft based in europe and only EU licensed individuals (pilots and cabin crew) can fly them, maintenance is local anyway from what i hear. But ownership and control might be an issue, although Austrocontrol is famous for its flexibility for cash.