Have not read every single post, but what I would do is first open the CU(s) and see if there are any harmonised cables in there.
Then I would turn all the circuits off and re-energise them one by one until my mystery outlet comes live. Then I would check if that circuit were a radial.
I would check to see how many conductors were connected to the breaker, be it a radial or ring final.
It could be an additional cable was fed from the CU to the faulty accessory, or to a point unknown from where the old cable was extended with H to its current position.
Another (rare) possibility is that (if the socket is fed from a ring final), there could be two breaks in the N at adjacent accessories (or the N element of a leg has been deliberately disconnected due to a problem) and the faulty point was tapped off this leg with a JB.
Picture the scenario. Attached to that spur is a faulty appliance.
Spark gets called to RCD trip fault. Cannot locate faulty equipment but isolates a bad reading neutral between two sockets which he disconnects.
I suppose powering down and connecting L & E together at the faulty accessory would give you an idea where the broken cable was connected to on the ring. Disconnect all the sockets and put the DMM on each leg to find the deliberately introduced LE short.