Actually, the more I think about this, the more I'd be surprised if there was a General Qualification that allows you to teach airside driving at any airfield. (Apart from the more specialist ramp equipment).
Surely the majority of the courses you'd be teaching would be very station specific. Certainly airfields vary a lot in terms of where and how you can drive, who has right of way, and what the local laws are.
Maybe the best way to become a trainer is to actually approach the station you wish to work at and approach them. As has been said, at Newcastle, the overall regulation is done by the Fire Station, at the BAA Airports its presumably BAA?
RTG!