Whatever anybody thinks about the EU, it is undeniable that the creation of the Single European Air Transport Market between 1993 and 1997 was a landmark achievement which could not have come about otherwise. In other words, no such thing (within the single market) as a 'British' airline, 'Irish' airline etc. Only community carriers, free to fly where they chose, as often as they chose, with whatever prices they chose.
Brexit would probably not change anything in this respect because it's already happened.