I fear we're going to be going round in circles shortly, but...
Liability is the responsibility of the land owner.
A land owner should, in law, take "reasonable" measures to minimise the risk to people who come onto their land.
Definition of the word "reasonable" is virtually impossible, even in a court of law, which makes life more difficult.
However, if a land owner assumes that they must take "reasonable" steps to ensure that people coming onto their land are protected from coming to harm, then that's a good place to start.
Similarly, the land owner is - to an extend - protected by the fact that they should only have to consider people coming onto their land and acting "reasonably".
That is to say that if someone who owns an adit fences it off and puts a sign on it saying "Danger, old mine, keep out", then they're probably covered against someone getting past the fence, getting in and damaging themselves.
However, if the land owner becomes aware that lots of people are climbing over their fence and gaining access to the mine, then the land owner's intent to keep people out starts to fall below "reasonable" measures and they may have to consider other means, for example gating the adit.
There's also another aspect to this in that if the mine happens to have a big vertical drop in the darkness, then the "reasonable" measures to keep people out should probably be a bit more serious - ie the measures taken should be proportionate to the risk.
In a case such as this, where there does appear to be a big drop inside the adit; and where there is reason to believe that people will gain access to the adit regularly, then there probably does need to be something done.
To my mind, "reasonable" measures would be some sort of signage at the adit entrance; and potentially a half-height wall across the adit a few feet in, with a sign on that wall warning of the deep drop beyond it.
The argument about grilles is probably correct: if something like bars were installed but one of them was subsequently removed so a child could get through but an adult rescuer could not get through, then the potential harm would be increased - particularly if the adit was below the high tide mark and time could become a critical issue.
At the end of the day, it comes down to a legal argument about what is "reasonable": did the land owner take "reasonable" steps to warn people of the danger and keep them out; and did the person gaining access behave as the land owner might expect a "reasonable" person to do.
Hello again darkness, my old friend...