EASA is an EU agency. Look it up on their homepage. EASA rules are applied by non-EASA members as well but they don't get a say when rules are made.
For those hailing the Swiss as a model, they have to copy a lot of (technical) EU Standards without having a say when those standards are set.
As for UK based companies setting up subsidiaries within the EU, depending on the agreements made after a Brexit they might be subject to ownership and Control rules requiring 50%+ EU ownership to have EU traffic rights.
If the UK (or at least parts of it) decide to leave the EU, it would most probably happen for the wrong reasons. I am not a UK citizen but I suspect that much of what has been written here and elsewhere about media influence is unfortunately true.
There are too many people all across the EU who try to make other people believe that the passing of the golden past is the EU's fault and that leaving the EU will allow a return to that (as was very fittingly written here mostly imaginary) past. That even works for countries with a communist past. The world has changed during the last 50 years and we take for granted that the EU has given us three quarters of a century of peace by making it economically unattractive to attack countries you're better off doing business with. If we leave that path by retreating to our own countries, "buying national", valueing locals more than foreigners, there might be a day when we perceive force to be a legitimate or even the only means to pursue our own interests. Look to Ukraine/Russia or back to the Balkan wars to see how it works. Living memory of wars within Europe is dying out rapidly but those people who witnessed it were the most enthusiastic supporters of European Union.
I'd be sorry to see you go but I'd still be against cutting you a "leave but keep all the benefits" deal....