I see only three 'actual' options for any cave to prevent damage by the 'caving community', based on the significance of damage/ease of damage ratio (e.g. a cave with important scientific features or amazing formations that can be easily damaged gets a high score, a cave without significant features OR where damage is hard/unlikely gets a low score):
1) close the cave (either completely or partially e.g. only open to scientists/4 trips a year/whatever)
2) leader system (obviously legal issues on CROW land)
3) best practice conservation work (taping, education, digging to avoid delicate areas, fixed aids etc)
Note this is only considering damage from people in the 'caving community', not the 'general public' - in some limited cases access restrictions may help restrict damage from the 'general public' but they do nothing to prevent inevitable damage from the caving community, which is probably the more significant cause of damage in UK caves.
Obviously a leader system on CROW land is tricky since the BCA holds a right of access to caves under CROW, at which point to institute a leader system you would have to make an application for restriction of access rights to Natural England, who won't issue the permit because they don't believe there is a right to access under CROW, at which point you could just stick the gate on it, but then you are going against your own BCA policy that such restrictions are illegal without the relevant permits, which you can't obtain...
What I really don't approve of is where a pretty area of a cave is hidden (perhaps by hiding the entrance to the passage under easily-moved rocks or similar) and not publicised, so that it is not found by other cavers, but the area _is_ visited by people 'in the know' (i.e. it is a club secret or whatever). Access should be for all or none.