The needs of Military SAR as I knew it when a RAF helicopter pilot, have evolved.
There is the 'conventional' onshore and maritime role, which is currently covered by RN, RAF and HMCG aircraft and crews.
And there is Combat SAR, highly specialised and requiring state-of-art equipment to maximise success potential. This is the area where military resources must be concentrated.
There is no reason to fret about potential contractorisation of military SAR units around the UK coast. Existing HMCG crews are highly professional and the airframes, though elderly, have a high standard of equipment, sometimes exceeding the spec of their military counterparts.
If you want to see a state of art civilian SAR helicopter, look no further than the BP 'Jigsaw' AS332 aircraft with an equipment installation designed by a well-known North Sea helicopter company. It's now working. (And, btw, if this had been a military project it would still be in the discussion phase!)
One final point: training. If you contractorise, you must make adequate (financial/contractual) allowance for both continuation training and the initial training of crews.