The police would probably 'own' the plan
Not probably but definitely. For any overland incident, the police have primacy (and, below the high water mark, the Coastguard) and will therefore notify - with minimal delay - any agency which can usefully assist. For a major incident like a significant train crash (such as the Grayrigg derailment), the police will set up their Bronze, Silver or Gold command and run it from there.
The problem is that, in many cases - Grayrigg is a good example - calling the 'obvious' emergency service may not achieve a lot. There were plenty of injured people in the Pendolino, but no ambulance was able to access the scene because of the lack of nearby roads. Because it was dark, the air ambulance couldn't attend either (and frankly, given the number of casualties, even a gaggle of air ambulances couldn't have achieved much). What the police did with commendable (but entirely normal) speed was to notify the Aeronautical Rescue Co-ordination Centre, who instantly dispatched three large rescue helicopters which were able to move a number of casualties at once (a fourth aircraft was launched later when a crew had been mustered). The police also put their own helicopter overhead to co-ordinate the movements of the rescue aircraft and reduce the risks of four aircraft operating into the same field in the dark. I seem to recall that the police also summoned assistance from several of the local Mountain Rescue Teams whose vehicles were better able to get to the scene than the usual emergency services.
While many incidents are less challenging, the best bet in most cases is to call the police and let them sort it out.