Got it, at last! (thanks dhillon, good to be reassured a little force wasn't going to hurt).
Put the new one in. Went for a spin. STILL DOESN'T WORK!
I have noticed something though. 16.5 blows hot. I turned it up to HI to see if (what was reported as 16.5) was FULL hot... I think it was, as near as dammit. However turning back down from HI to 16.5 gets me cold air. Hurray! But only for a couple of minutes. Boo! It creeps back up of its own volition to thermo-nuclear, whilst retaining 16.5 on the display. Setting it to LO blows proper cold air for as long as I want.
I'm sure I've read somewhere that disconnecting the battery for a few minutes might reset something or other. I will try that this evening (I've got screwdrivers here with me but no spanner). But if that doesn't work... what is my next step? The outside temperature sensor, which I believe is in the wing mirror, is reading 11 degrees C in the console display so I'm guessing that is okay. Am I likely to need a new climate control panel? Or is there something under the bonnet that might need attention?
Edit to note that I understand 16.5 is higher than 11, and in that circumstance I would understand a *bit* of heat... but until this went wrong recently I have never noticed it blowing hot quite so vigorously in 5 years of owning 2 156's...