That does look like concentric cable, rather than twin with all the red insulation missing. Inner conductor, plain rubber insulation, outer conductor, cambric tape and compounded braid sheath. Very rare stuff, I've been collecting cables for 30 years and never seen any of that before.
Interestingly it appears to be 7/.029, going by the size relative to the JB terminals and the fact that .029" was the smallest strand generally used in non-flexibles. This is a larger cable than needed for any normal lighting circuit and, allied with the fact that this type of cable was rarely used in domestic work, I wonder whether it was installed separately to the original installation perhaps as a repair, by someone who had some surplus on hand.
Concentric cable achieves its compactness and enhanced rating in part by having reduced or no insulation over the outer. This imposes the requirement that the neutral conductor is reliably earthed which was not always done until after the war and the amendments to the 11th edition, and sometimes required permission from the supply company. Use of concentric wiring would tend to be a deliberate choice, very often following a proprietary system, not one made on a whim by the installer. It might have been done to the specifications of an engineer who was personally keen on the idea, more likely in the 20's than 30's.
I would be very grateful for an opportunity to save whatever of it you can get out intact, for the museum. Old rubber cables don't always withstand removal without crumbling, but the longer the pieces you can get, the better. I will happily pay for you to pack it in a box and send it down. Even if you can only get short stubs as samples, they are still interesting.
In the meantime when I am next in the museum store I will try to find a reference to it in a catalogue.
