The call out procedure as recommended by BCRC is dial 999, ask for police and then ask for cave rescue. That assumes you have a person dialling 999 who knows what they are doing. However, the formal call out procedure as is advertised in BT phone books is dial 999 and ask for cave rescue directly. Unfortunately the 999 operator so rarely got asked cave rescue (or mountain for that matter) that they often fouled up dealing with the call. Hence BCRC's recommendation.
But if the person dialling 999 did not know who to call, then I suspect the 999 operator would put them through to Fire & Rescue. Whilst (don't ask me why) in the Forest of Dean this would be OK as the local procedure actually goes 999 / Fire & Rescue / Cave Rescue (at odds with BCRC's statement); for every where else I suspect that the Fire & Rescue operator on receiving the call will not be aware of cave rescue and just deploy their resources. So hopefully, you eventually get a congregation of blue light vehicles at a cave entrance and someone who recalls, 'ah yes perhaps cave rescue could help'. Sadly that did not work in one case and the person died, see
http://www.scotcourts.gov.uk/search-judgments/judgment?id=eca78aa6-8980-69d2-b500-ff0000d74aa7 . So yes I can see the poor firemen who turned up saying 'how on earth do we deal with this' and calling for back up resources. And I am not going to blame them for doing so - after all would you recall a variation in a routine you were perhaps briefed on a year or so before which you had never used? Or trying to avoid having to stand up in the Coroner's Court and explain why things went badly.
It is worth noting that of the tens of millions of 999 calls made per year, only a few thousand relate to cave & mountain rescue. So it is not surprising that operators do not recall the process for cave or mountain related rescues. It is not helped by there being around 50 different Fire & Rescue Brigades, each with their own script for handling a 999 call.
But if you know what you are doing and follow the procedure, then the police 999 responders should be aware of cave rescue and should institute a call out so only MRO or whoever turn up plus perhaps one police car.