AT would have a set procedure for calling the emergency services and to be a little bit fair on them we don't know of the qualifications of their own first aid responders, they could well be trained to paramedic standard.
I agree with Sam, in this situation I would expect the park to control the situation and decide if a 999 call needs to go out.
AT is a controlled environment and not a public place
I think i can answer this.
Alton Towers Medical (ATM) has Emergency Medical Technicians, (Ambulance crew qualification). They have a direct link to WMAS (local ambulance service) for doing CFR (community First reponder) work in the local community.
Any public 999 calls to WMAS from inside the resort would be redirected to ATM, then they would feed back for extra resources (If required) . although if multiple call came in to 999 saying there was a crash between two trains on a ride, WMAS would start getting ready for the resource call from ATM.
This can be overridden by a Qualified member of the public (WMAS staff, some SJA/BRC members) that have major incident training. and can give set information to the WMAS control along with their ID code.
Update to post.
I have been told ATM works long the same lines as the volunteer First aid Organization i belong to. so here is a rough idea on how it would work. ( I am doing major incident below, as it fits the question)
ATM is called to scene. they assess the situation on arrival. If it is a major incident one of them will contact WMAS with the reverent Major incident information whist other members of ATM are treating ( if possible )
There will be a member that is in overall control, (this could be security or ops manager) they job will be primary incident control. e.g. safe working area, safe vehicle access, etc.
AT Incident controller will usually deals with supporting emergency services, when a senior officer arrives from each service on site. like securing the lawn for aircraft landing.
11 mins from crash to call to WMAS does not look that bad when you know the major incident protocol. The one question i have is how long was the time from crash to ATM being alerted and getting to scene, as that is the real start time for medical assistance.