No, that isn't modern heatshrink on the dial cord. It's the old type of sleeving, hard to describe, but like a braided rubber, and quite original.
The induction coil forms part of the anti-sidetone circuit. It couples audio to the receiver, and also reduces the volume of the callers own voice in the earpiece, which would otherwise be loud compared to the incoming audio from the distant end.
As I remember Paul, your telephone number was written on a small disc of paper that fitted under a plastic disc in the centre of the dial.
Here you go:
http://www.telephonesuk.co.uk/dial_labels.htm Could be fun fitting a BT connector to the end of that braided flex.
You think I'm even going to
try?!
I'll be fitting an old 1/4-inch plug and making up an adapter lead to go with it.
But you're very warm.......