alanl – thank you so much for the step by step. I will have to do it in the morning as the tank etc is literally just by my daughters bedroom and she is now asleep.
There is only one cutout on the immersion – a small pip on the thermostat and that has not tripped.
The immersion is on its own RCD on the main board and was off when I did the tests (excepting the first one measuring the voltage. The resistances all measured with the RCD flicked to off)
The thermostat and element is this one – tesla incoly 14
The thermostat has two tabs on the back which slot into to the L and N on the immersion coil and then have the screws on them for the brown and blue wires.
I have double checked the earth is secure.
When I have the RCD set to on and power to the thermostat, with the thermostat set to 60, voltage across the L and N is 230.
It sounds like you are the exact sort of expert I need – if you are anywhere near Brum/Stourbridge might you be free for a job?
I will do the other tests in the morning.