[dnnrly]

I don't know the exact rules but in the UK, when calling 999 you're asked which service you require. Fire service will only get police involved when they need it or automatically when more than 2 Fire Engines are dispatched. Ambulance calls can result in an Ambulance with a crew of 2 or a single paramedic in a sensible estate car (station wagon) with a big engine, they'll call the Air Ambulance if they need one and it's free. Dispatchers will send who they think you need as they see fit. That includes Lifeboat Service or Mountain Rescue. Or Police, of course. Each service will obviously ask for backup as required.

The BIG difference with what you've described though is the layout of the UK is much denser than USA. The resources available and the nature and frequency of call outs will obviously be quite different.