I've given up - end of story. Let it soak with some WD40 outside and inside. Hit the outside with boiling water. Still won't budge - just bends the mixer pipe behind the tiles. No new flexible hose shower head for us.
But yesterday I went back to my old place (kids living there) and easily pulled the head off the shower unit there to do effectively the same job - no problem and it had been in place for about 9 years! But I know the mixer head is well mounted to the battens and nothing but teflon tape was used - I was owner-building and was a pain of an inspector of the tradies' work!