[MovedGoalPosts]

Turn off the main switch by that digital meter. See what goes off - power sockets, lights etc. If nothing obvious, then leave it off and see if someone starts banging on your door?

In the analogue meter picture, you can see the mains intake fuse below that trunking. A meter is above the trunking, but you don't show the fuses related to that meter. On the bottom right of the picture you can see a heavy cable dropping down to the floor, and that probably goes to your alternative digital meter? Take the trunking face off and you'd perhaps trace that, but don't disturb that as you are not an electrician so don't know it's safe to do so (if you were capable of knowing it was safe you wouldn't have posting this thread).

As a secondary issue, if your landlord doesn't know what these meters do, and given the older fusewire style wiring with no indication of a RCCD, or even trip fuses, plus rather feeble earth bonding, I would doubt whether the installation meets safety standards. If the landlord is letting to a shorter term tenant he will have a duty of care to you. He may not have a legal requirement to have a recent electrical test, as these are recommendations, but he is prudent to have done so as he could be liable if you were to suffer an injury due to some deficiency. Ask him for his test documentation, as you are concerned that he does not know enough about the system to know that he has let the property to you in a safe condition.