My 4×2 has been in action again, trying to find the remainder of the mystery sometimes-4mm/sometimes-2.5mm/sometimes-1.5mm cable. It finally appeared in the tiniest gap possible between back wall and joist.
As we had suspected by tracing everything else, the junction is an unfused union of all three cable types with a 230V 32A circuit breaker on one end and a light switch on the other. So in the event of fault current at the kitchen lights, the 1.5mm cable is definitely going to burn out and almost certainly set fire to the flat roof. Delightful.
It is no longer like this.