As usual with BREXIT the problem is really fractal, the closer you look, the more complicated it becomes.
Upon leaving the EU without a deal the UK would also leave Eurocontrol, EASA, Euratom and a quite large list of other agencies and treaties, amongst others the EU open sky agreement, the open sky agreements with the US and other parties. What would that mean?
All EASA licenses issued by the UK CAA would no longer be valid and recognised anywhere world wide with the possible exception of the UK.
The UK and its airlines would no longer be able to access Eurocontrol, the slot system and any air traffic control agreement under that umbrella would be null and void. Doesn't matter, the ATCO licenses are no longer valid anyway.
The UK airlines would have no route rights into europe at all, nor into the US unless a new UK-US open sky agreement has been done. Initial talks on that matter were, well, quite sobering for the UK.
No UK aircraft would be deemed airworthy if the airworthiness certificate was issued by the UK CAA or under UK CAA guidance.
Of course, any completely UK or third country certified (not based on EASA rules) aircraft and aircrew would be able to overfly EU countries and even land in the EU under the montreal convention, but they would not have any airport slots nor route rights.
That is all based on a no-deal scenario. It becomes more likely right now, but there is still a slim chance for a hastily done deal, although for that the UK would have to completely cave in as the EU is not in any way able to get away from its red lines (integrity of the single market system).
The only UK airline that has tried to prepare for BREXIT in its reality so far with shifting a third of its fleet into a european AOC. However, with the very small exception of the recently hired TXL based crew the rest of the airline is completely UK certified. Which means it will be effectively grounded with a small number of flights being able to be operated out of TXL.