Err, the Govt paying for a service every year is a hell of a lot cheaper than paying for the total re-equipment of said service in one year, i.e. this year.
Which is the scenario the Govt has been faced with for the last 5 years of this saga.
Bristows are either funding the acquisition of the helicopters through their own capital assets, or via debt (or some combination). In the first case, the Govt doesn't have the capital, in the 2nd, it can't borrow more. Bristows will recoup their costs through the contract charges annually.
As with so much procurement, the Govt is moving to a basis of paying say £20 per year for ever, rather than spending £100 every 10 years and £5 in intervening years.
It is almost certainly more expensive over say a 50 year period, but from a cynical perspective it is cheaper over the next 3-4 of that administrations expected lifetime.
Less cynically, it is what nearly all major companies do which is lease their site/equipment because it makes planning of finances vastly simpler and less cyclical, albeit at a cost. Although even that is mitigated by the future value of the cost, what you can do with the capital cost now and above all, by how the risk the entire thing represents is thus reduced (well, should be !).
I kind of prefer the Govts approach because it is more honest in a way - it avoids the scope for politicians to delay/cancel capital projects that are up for renewal in order to use it for short term electoral bribes in their personal favourite areas - because they can't raid the capital fund because it doesn't exist and everything is being paid out of revenue - and because you can also more easily understand the true lifetime costs of projects/services that a more cyclical nature hides.
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In the 60s and/or 70s I believe there were such demands, and the RN wasn't in the financial strength that it now is - certainly I recall being told by a RNLI official that they had had to fight the proposals at the time and it had come quite close.
Certainly today they appear the world's premier maritime SAR service, and indeed, with so many "Air Ambulances" funded (at least partially) by charities, one does wonder if the Helicopter SAR side could be similarly operated rather than being a Govt funded service ?
An interesting charity the RNLI, and one of the few I support as I think they actually use most of the donated money for productive stuff that you can see, and haven't gone down the "pay huge salaries and spend lots on PR and lobbying" route of so many others. I just wish I was able to live close enough to a station to volunteer as a lifeboatmen !