But what I meant by the comment above is it's my understanding that E7 is not really used these days. It is difficult to control heat output, expensive units to install, tariffs are expensive.
Correct.
E7 is somewhat cheaper overnight, but the day rate is significantly more.
Modern storage heaters have the same disadvantages as old ones - only of use if you want to heat the building all day, every day. In the past plenty of people did. Today not so much.
Having the hot water on a timer might at least allow exploration of overnight cheaper rate electricity tariffs.
Not worth bothering with - hot water energy use is tiny compared to heating the building.
Theoretically of value if storage heaters are also in use, but only because you might as well have the hot water with the storage heaters if E7 is there.
There must be an 'official' way this type of thing is done in electric only apartments. That's what I'm looking for
The usual method is heaters with individual thermostats and programmable controls built in, most of which can be controlled via some smartphone app in various ways including grouping them together.
Some require a central hub to work like that, others not.
In the past there have been systems which can control multiple heaters from a single point using a 4th pilot wire in the mains wiring, but those are pretty much obsolete now that everything has gone the way of apps and smart junk.
smarter way to control the existing panel heaters and hot water cylinder by adding thermostats and central programmer.
Possible with various control modules such as the Shelly range of items, all this will still need a smartphone. However if you are looking at renting, this is not a viable option, as you will need an EPC for the property and if it's been fitted with non-standard or home made type controls, those won't be on the assessors software and will be rated poorly.
Is there an immersion heater timer/programmer that can control the two elements in one unit?
Yes, the Horstmann BX2000, but that is only of use if you have E7 with a switched output from the meter, and it's already wired with dual circuits to the immersion heater. It doesn't really control anything either, it just shoves the E7 supply to the lower element when that supply is powered, and allows the use of a boost function from the other circuit for the top element when the E7 is not on. Can also be used with a single element from two separate circuits if needed.
No use without E7, and not a great deal of use even when E7 is there.
Hot water heating is mostly irrelevant in terms of control - if the cylinder is a modern well insulated one, the difference between leaving it on all the time and switching on/off is minimal. Modern cylinders will retain the hot water for a day or more.
If it's an old poorly insulated one, spend the money on a new cylinder rather than fancy controls.