As with all government projects/privatisation, it all depends on how well the contract is written. Private rescue organisations are used and work effectively in other countries, so that’s not to say they can’t work well here, if implemented properly.
It is also worth noting that the purpose of the RAF SAR is to rescue downed aircrew, not civilians, this is simply done as they are the best placed to do it, however if a pilot bangs out somewhere that will be the priority. Military craft also have much higher standards with regards to mechanical operating and maintenance and as such can often be unavailable (I was on exercise with a MR team and we were due heli training but the SeaKing couldn’t attend due to a possible fault relating to military electronics – nothing to do with actual operational efficiency of the craft in civilian SAR).
As has been noted though, I’m unsure how the willingness and the skill levels of a civilian team would perform, the ability of the military SAR crews is just downright gobsmacking.
I think in an ideal world it would be good to see the RAF essentially ‘paid’ to provide a dedicated civilian SAR service, both providing SAR capabilities for civilians whilst also giving them valuable training.
Time will tell.