Actually when all else fails, I prefer the dremel drill with a circular cutting disk. It's more surgical !
At any rate the mystery is solved
. I cut the handle as I described above and got:
the plastic handle: a small piece of a metal cylinder that has barbs on the outside and a screw thread on the inside, a nut.
So obviously the T handle is manufactured with the metal cylinder inside it. This explains why I could twist the handle around and around and make no progress: it was just twisting around the barbs.
I think it would have been VERY difficult to have popped the handle off the metal cylinder as the latter has the barbs.
As it happened, the metal piece was so corroded I couldn't undo it from the rod, so I had to cut that as well.
At any rate, I have moved the cable to the hole I want it in. Now all I need is a new T handle ! From where ???? !
Thanks for all the responses. Hope we've all learnt something !