when I had a house with a 1920's supply cable in outer London, looking like the OP's, there was a wound-on steel "bandage" armour (which went rusty in the ground, might originally have had bituminous paint), and a bituminous cloth bandage, inside which was a lead sheath with two conductors (I have an idea they might have been wax-paper insulated).
An electrician had previously incorrectly put a pipe clamp on the armour, but when a new meter was fitted, the iron service-head was replaced with modern grey plastic, the fitter stripped back the armour and put an earth clip on the lead sheath. I had an idea they would change it to PME, but I don't think they did. I wrote and asked if they would, and they said yes, but only if I had an EICR done first.
I think the iron head originally provided some kind of earth as it must have clamped the steel armour and the lead sheath.