After accidentally trashing the original RF lead for the ZX81, I ordered a new one but in the meantime thought I'd see if I had any suitable alternatives knocking around among the random AV cables I've kept. Finding a phono to SCART convertor, I thought I'd give it a try:
... and was surprised to see it work first time - no tuning required either:
I did try the new RF lead when it arrived but never managed to get the TV to tune in so have now abandoned that and am sticking with the SCART.
All looking good except that half the keys don't work...