It's difficult to diagnose the problem, but certainly working with different rescue departments seems to help the problem.
I would argue that in yorkshire the problem of calling the "wrong people" is non existant.
Firstly, because mountain and cave rescue are the same thing.
Secondly, because all the emergency services are a close knit group.
Derbyshire is similar, I guess?
Firstly, the buxton base is home to fire, mountain and cave rescues.
Secondly, because the groups are on the same base, it would be hard for a fire or MR vehicle to pass by the DCRO hq without thinking: "hang on a minute, we're going to a cave!".
They are two very precise examples of where the groups work quite closely with others. In derbyshire we have also had hands on experience of incidents where HART have been called out alongside and we've shown them various different aspects of cave rescue. I believe we now have mutual respect for each other. but i'm sure they would ensure cave rescue were at the scene in the case of a rescue at a cave.
I have no idea of the set up of mendip rescue.
1) how their training works.
2) how many members are trained up and would be called out in an incident. (Would particular members get preference over others, if a new member turned up would the others know their strengths and weaknesses)
3) how an individual or cas care trained rescuer from another base could join.
4) where their base is.
5) how much they liase with local emergency services.
6) how a general member (if they exist) progresses towards being a warden.