The problem is that the UK is broke and can't afford the capital to replace the old up for retirement Sea Kings with S-92s
There are two options, lease or finance the replacement aircraft or privatise the whole thing and pay monthly for a service. It looks like privatising the SAR service also helps to downsize the military, which is also happening as a result of budget cuts.
The UK public need to realise that the old days of Britannia and her Empire are over.
How many people in the UK would willingly pay extra taxes for SAR which 99.9% of them will never be in a position to need or use?