Actually the CAA is not our regulator, EASA is. The CAA is a "Competent Authority" under EASA/ EU legislation.
If you think this is going to go away this morning forget it. Due to my job I spend a lot of time on EASA stuff and in recent meetings where we've all been laughing about will it all matter on the 24th May.
While the vast majority of CAA income is derived from CAT operators the CAT operators will have the biggest say, for anyone with an AOC then remaining EASA is the best option, and like Norway and Switzerland you can be a member of EASA while not being a member of the EU.
Lets face it, if BA, EasyJet, Monarch etc decide EASA is their best option then their collective voice will be a lot louder than LAA, AOPA etc. In aviation terms BREXIT won't affect much, if anything.
SND