Even if the UK did send a few F3's & Typhoons to Georgia, (Which I very much doubt), their first choice would be the Typhoon, the F3's would probably be kept back like they were in the first Gulf War. But the F3 now is a different beast, better than what it was back then.
Anyway, its their problem, if they're big enough to start a war with each other, then they're big enough to finish it themselves. Let them sort their own problems out.