i was told...
that the reason we have to carry civilian clothing is because our Strat AT flies (sometimes) via the civilian airports in the Middle East, before going back to Blighty - and you could remain in compound (in uniform), or go into town (in civilian attire) - given those options I think bringing some civvies is worth it, as a Crab Air Stalag 18 compound is no fun on return from SANDGHANSITAN!
On the subject of wearing uniform in the UK civil airports, it is worth remembering that active terrorist cells collate information on us military types, so advertising yourself might not be the cleverest move. Shame I know, but the fact remains bad guys want to do bad stuff to us and ours.