As an aside, Treliske Hospital is in Truro, Cornwall, which leads to a very long transit. Up to not very long ago for a job like that a yellow (or grey/red RN) helo would have been the most likely conveyance, although the NHS would probably have been charged under the arcane and quite mysterious Treasury rules. Now of course SAR is a civilian organisation (as is NPAS) so, by the sounds of it, the lines are getting even more blurred.
However, as NtD alludes to below, is this a sensible usage of police dedicated resources? Who would have picked up the pieces if there was an urgent police requirement in the west? I'm only an interested bystander now but it seems to be a dilution of the task (or maybe just additional tasks being added piecemeal).
Equally of note, during my time on SAR in Norfolk (showing my age as this was many years ago) we provided a lot of assistance to the police in searches and the like, and led to very close cooperation. This usage of course did not appear in any police stats as it was almost all ad hoc; unfortunately it ceased almost as soon as police helicopters started appearing