The 999 calls are processed first by the ambulance control rooms who allocate an appropriate asset (theirs not ours). A really switched on controller might recognise from the location that a SAR helo might be the best option but more often than not they don't (can't really blame them it's not in their job description).
The first ambulance asset on scene which might be a first responder, land ambulance or the air ambulance can then assess the situation and then make the call for the SAR helo.
It might not be the ideal solution for the patient as the process can take a few hours between initial 999 call and the SAR helo arriving which, if you are broken and bleeding on a cold hillside or similar, will seem like an eternity. However, it does usually mean that the casualty gets medical care quickly unless they are in a really inaccessible place and then we are just used for the extraction.
Through liaison we try to remind the ambulance crews of our existence (generally the AAs are very onside but the control rooms can be very different in their view of us) and it works across most parts of the UK.