Body sized hole in bathroom escape – Who pays?

I have to ask: Was she drunk?

Seems like a no-brainer to me. She is.
This will be a very tedious fight with lots of time consuming ridiculous arguments.
I suppose you had better get independent evidence that there is nothing wrong with the door and that there is no evidence that there ever has been.
For the sake of the other tenants and you relationship with them, I suggest that you get the wall fixed ASAP and bill the tenant formally.
Then set matters in motion when, inevitably, she does not pay up.
I do not think that this can undermine your case, but you could consider a bathroom door lock that can be opened from the outside in an emergency. They are very cheap and they require a large screwdriver or flat blade to turn a large screw from the outside.
Of course this then leads to the possibility of silly objections regarding privacy but you would just have to live with that.
Students are lucrative & harder work than much of the market.
On the basis of the evidence submitted, even if she were drunk, she is clearly an idiot and there is no reasoning with such a person.
Obviously there should have been someone to contact in such an emergency and if this was not done, then why wasn't it?

Not many students go to the toilet without their mobile (not that I have studied this!). Very suspicious!

Seems to be a bit of a discrepancy here. If the door and the lock were in perfect working order, why couldn't she get out?

The door locks that open from the outside with a screwdriver slot can actually fail, they have been designed quite ill thought, I have been locked twice, luckily my wife managed to pass me the bits that fell out from it and then I managed to open the door.
The silly oblong knob that is held on the square shaft is held tight with a grub screw, if this screw ever comes loose , you could find that as you closed the door, the rear part that has the screwdriver slot is permanently attached to the square shaft, which can slide out leaving the oblong knob disconnected from it, or the oblong knob simply comes away in your hands as you shut the door and as you tried turning it to locking position, I managed to shut the door and as I turned the knob it managed to lock the door as the locking bolt popped out into locking position and the knob just came away in my hands.

I then tried to refit the knob from the inside on to the shaft, but in doing so the shaft got pushed further back and fell out on the other side of the door! I was locked in for a good few minutes until my wife barely heard me.
I also experienced the same again in one of my rented properties, where I was almost going to lose the knob again, had I been locked in this HMO, bathroom, there were no tenants at home, and I left my mobile phone on a table, as well as there are no windows on this bathroom, so I would have been pretty locked infor a good 4 to 6 hours!
It is possible that her lock did go wrong and then someone else may have refitted and tightened the grub screw.

Reply to the comment left by Mike at 29/02/2020 - 12:16
That's a new one on me, but fair enough.
Perhaps a better quality / design of lock is required?

Reply to the comment left by Paul Shears at 29/02/2020 - 12:33
Normally if the grub screw on the oblong knob is well tightened to the square shaft, it should not loosen up in its life time, but if a builder used a bad screwdriver or ill-fitting hexagon key wrench, teh screw could eventually start loosening and that is when the knob can fall out, a good design would be where the square peg is pressed on the shat and the grub screw is then used on the outer slotted part, such that if this screw came lose, the knob is still held on to the shaft and one can push this shaft back into the lock and open the door.
Another issue I found with these types of locks is the knob is not too big to provide enough leverage against a slightly hard to turn mechanism, especially children can get trapped as they have not got enough strength to turn a small knob which may have become more tight to turn over a period of time.

Reply to the comment left by Neil Patterson at 27/02/2020 - 15:11
Unfortunately, who could know such a thing.

Reply to the comment left by Paul Shears at 27/02/2020 - 18:54
Unfortunately the tenant hadn’t taken their phone with them into the bathroom, so couldn’t call for help. We are looking into new types of locks.

Reply to the comment left by Rob Crawford at 27/02/2020 - 23:22
It was one of my first questions, to ask if the tenant had her phone.