Although the plan is that approx 2/3 of the public costs of SAR-H will come from the MoD 'pot', with the other approx 1/3 coming from (I believe) the Dept for Transport via the Maritime and Coastguard Agency (MCA), it's important to remember that 100% of that money comes from the taxpayer; it's all public money that will go to pay for UK SAR irrespective of the government dept that it flows through to get there.
Why would it be done this way, at least in the early years? Well, consider this: SAR-H has to be on contract next year in order to be up-and-running in 2 1/2 years' time. To attempt to change the SAR-H funding flow to a single government dept instead of the current situation would involve a fairly hefty amount of departmental bureaucracy (UK government depts are not known for their speed and efficiency of action), which would seriously jeopardise the chances of SAR-H being able to get underway on time. The simplest way to remove this risk to the programme would be to keep the current routeing for this public 'SAR funding' until the project is in place and providing the UK SAR service. Once this is achieved, and assuming that a single government dept is considered to be the most appropriate routeing for SAR-H funding, then the necessary bureaucracy can get under way with the 'fait accompli' of SAR-H already being extant rather than in a vulnerable pre-contract state.
As I heard someone describe it a little while ago, Private Bloggs in Helmand won't go short of body armour just because 2/3 of the public SAR-H money happens to flow through the MoD.
Louis