I haven't measured the resistance, but certainly when you switch it
on, there's very little response from the little turny wheel in the
electricity meter. I used the same wiring on the top immersion heater
and it works fine, so I'm pretty sure the actual heater's kaput.

That isn't enough to be sure. Frequently it is the heater's internal
thermostat that blows. These can usually be replaced without removing the
immersion. It is worth checking to see, even if it does turn out to be the
element anyway. The thermostat is usually a long thin rod that slides into a
tube visible when you remove the cover cap.

Christian.