You need to know:
Is there 230V at the immersion heater terminals (not just at the thermostat)
What is the resistance across the heating element
turn off the power first and test for dead
Okay, well if (if! lol) I'm using the meter correctly, there is indeed an electrical problem.
What's the test for dead referred to?
With all the relevant electrics switched off, and wires disconnected, I show 19.6ohms resistance across the two non-earth terminals (labelled Neutral and T? what's T?). I believe that's the correct method, I have no idea if that value is what you expected or not?
Reconnecting all the wires (and sadly breaking one screwdown on the thermostat) switching all the switches and trips back on, I've then measured AC voltage across all combinations of the live and neutral wires, and the live, neutral and earth terminals (earth is irrelevant here right?) both before and after the thermostat. All readings show 0. I also rechecked the fuse in the airing cupboard with the meter, and it's not blown.
So, if what I've done is correct, then this means that power isn't reaching the immersion unit, and the problem lies somewhere between it and the distribution board with all the trips?
I can test inside the power switch in the airing cupboard, but beyond that the wiring is all inside the walls/floor, so from that point I'm stuck.
The fact the 16amp trip doesn't fail means this is okay I presume. No possibility around that?