why bother with the 13A fuse then, just connect it direct to the 10A circuit with a flex outlet plate. ( I presume it's so you don't have to get under the bath to change the fuse? )
Apologies for only part quoting, as I am only commenting on this part of the quotation I believe I am not misquoting or taking it out of context.
Its very obvious the left part of the cable has suffered severe heat damage, the right part of the cable has suffered only minor heat damage. In my opinion therefor the heat source was in the grey box (which I assume is the meter) to the left of the picture, not in the cable itself.
Fortunately this is on the suppliers part of the cct so their liability!
The same effect can be demonstrated with a heat gun or blow torch!
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