Mains seems fine. It's 22mm most of the way from the main up to the
tank. The last few metres to the shower is 15mm as with the hot but I
doubt that's the problem.

Do you have high pressure? It is possible that a PRV (pressure reducing
valve) just before the shower could allieviate some of the problems. Set to
about 1.5 bar (or as low as you can with satisfactory performance of the
shower), it will ensure that the mains doesn't fluctuate, provided that in
the house pipework it remains above the set figure. It will only work if you
have a high, but variable pressure.

Even raising or lowering of the shower head caused the temperature to
drop or rise by a significant amount.

This is more worrying, but with a low head to the hot side, I suspect that
the pressure change in the hot supply upsets the venturi.

Christian.