Using an Elson Coral E Water Heater

Just after a little advice. I've moved into an apartment where the hot water is provided by an Elson Coral E unit. This does not have a timer wired into it and does not have the immersion heater device on it either (as far as I can tell).

From what I've read this does not actually heat up a tank of water like a traditional hot water tank right?

At the moment it appears to be switched on all the time, so will I use less electricity switching off say during the day whilst I'm at work, or will it actually use more electricity getting back up to temperature when I switch it back on at night?

Of course, if my electricity supplier actually made my smart meter work I'd be able to tell, so that's not really an option.

It's a thermal store, where a fixed vessel of water is heated, and then cold water is passed through a heat exchanger to heat it using the stored heat.
The water inside which is heated is entirely separate from what you get out of the hot taps.

Intended to be heated overnight on Economy 7 cheaper rate electricity, and usually the switching would be done by the electricity meter or a device connected to it. Typically found in properties with storage heaters as well, which would also be switched on overnight only.

If it's on a smart meter with single rate and switched on all day, it will cost a fortune to run.

Thanks for your response Flameport, that's really useful info. I'll try turning it off during the day and see how that affects my bills. Hopefully for the better.