The top immersion heater will only heat the top of the tank! Natural
convection ensures that there is always a temperature gradient from the top
to the bottom of the tank. If you only heat the top, the top section can be
hot enough to turn off the heater by means of its thermostat - whilst the
bottom of the tank remains quite cool.

Yep, I was half expecting that. I've just turned up the thermostat by
a couple of notches and that seems to make it kick in again. I
understand I'm not going to have convection currents on my side this
way, but I imagine conduction through the water and the tank body
itself will help to at least partially address this.

This is fine for handwashing or the odd shower - but not a lot of use for
baths.

Well I've successfully run one bath from my new set-up! I'll have to
try again tomorrow in the evening after the hot water's been sitting
around all day.

Is the bottom heater definitely dead? Have you measured the resistance of
the element with a stat removed? If this is open circuit then it pretty
certainly *is* dead. Otherwise, it may just be a wiring problem.

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.

How did you try to remove it? You will, of course, have to drain the tank -
but it's easiest to *loosen* the heater whilst the tank is still full of
water - so that the weight of water stops the tank from moving while you are
applying a *lot* of torque - probably by sliding a tube over the handle of
the spanner to increase the lever arm length.

I got one of those box spanners and applied a hairdryer for a while.
Nothing happening apart from some a few groaning noises. I'll drown it
in WD40 and see if it's any more cooperative tomorrow.