Don't confuse JAA and EASA. JAA was open to all, EASA is an EU agency and their regulations are based on EU laws. The core of FTL is an EU law that required consensus between the EU parliament, the commission and the council of transport ministers. EASA is allowed to detail this law with their own certification specifications and acceptable means of compliance.
Without EU membership you may comment proposed changes to the basic law but you won't have any MEPs or ministers or commissioners having a say in it. So the CAA would be no better off than Joe Pilot writing a comment (though their comment might get more attention).
Don't bet con CAP 371 coming back. If EU-FTL means savings to the airlines, they'll probably lobby for keeping it, stating they can't bear the dual burden of a return to CAP 371 and losses caused by reduced market access, a weakened pound, whatever.