Ok lets list the current forms of access management, some caves/mines are a mixture, actually this is handy for getting a better view of how much is restricted or not.
gate + key + leader + permit + fixed date written request = Some FoD
gate + key + leader + permit = Charterhouse, cuthberts
gate + key + permit = GB
gate + key + leader = White pit
gate + key = Cuckoo Cleeves, rhino, Longwood?
gate + Bolt = Box, Derbyshire, Cumbria, ideal for Cuckoo Cleeves
Difficult Access (SRT, ladder, wet) = Brewers Yard (its a bit tight getting in?), (This option should be used more)
Open access = Swildons, Goatchurch, sidcot, Cumbria
Gates were they are needed, difficult access to Open access were gates are not needed. Less of this "incase someone trips over while climbing over a fence after two fields opening the hatch" scare tactics to lock things away.