Sell it, its not core military tasking
Yeah right - try telling that to the QRA guys during the Cold War hoofing it up the North Sea in the dead of night in weather that would make Michael Fish wince. QRA may not be scrambled as often as they were back then, and there's certainly no air war going on in the UKADR that requires the services of the SAR fleet to rescue dozens of downed drivers, but would you really want to get rid of them??
It would be fairly short sighted to get rid of that capability as once it's gone, it's gone for good. It may be OK to farm it off to Bristows in the short term, but surely SAR is one of those areas that requires experience? Plus, I would have thought that a lot of the Coastguard drivers are ex mil SAR drivers anyway. If you get rid of the mil SAR function, eventually all the current SAR experience would dry up and wouldn't filter through to the civi side; then, in 20 years time when the current experience has gone, you'll be faced with a bunch of inexperienced drivers flying in conditions that would leave the rest of the RAF's drivers tucked up in the bar.
Is that what you want - a baby driver that's only just got his ticket out in a gale trying to find a life raft bobbing about in the North Sea with a 30kt crosswind running close to fuel minimums thinking bugger, we didn't do this in training last week?? I would have to say that anything that keeps crews alive by rescuing them and getting them back in the air again is a core military fuction - or do we now have so many aircrew that losing the odd one here and there doesn't really matter?? Hmmmm
Plus, should we ever see the light and develop our own proper CSAR capability, could you really see Bristows volunteering to dodge bullets and MANPADS out in theatre?