I'm also shocked that 4 electricians haven't been able to play a fairly simply game of "I wonder what is supplying this" and make a little progress.
@MeganS I'll try and repeat what others have said in simple terms. As far as I can tell the original design was that the very right hand bit of your consumer unit is designed to be powered only during off-peak times.
So it looks as though the original design was for the storage heaters and the lower immersion to be powered at night.
The upper immersion was probably intended for obtaining extra hot water and likely was intended to be manually switched on and off as required.
(to complicate matters some modern storage heaters can also be wired to also be used during the day, but ignore that for now)
The primary goal for any electrician (as said above in various ways) is identifying how the off-peak supply to the lower immersion was intended to work when originally installed.
I'm 99% sure there is a cable from the consumer unit to one of the two marked switches.
I'm also fairly sure that it isn't now connected to where it was once connected, as the breaker is missing.
I could speculate that if the lower immersion became faulty, someone could have decided the fault was it wasn't getting power (mis-diagnosis if they checked during the day) and decided to give it power from somewhere else.
But any electrician is simply looking to find the cable that was originally connected to the very right hand space on your consumer unit, check which switch it goes to, and check that in turn is connected to the lower one.
They would need to re-fit the missing circuit breaker (MCB) too.
Once that is done, we get into secondary issues, like does the immersion heater and it's stat work, and how is the on-peak unit powered. But at least the on-peak could then be turned off to immediately save you some money.
If you don't mind, post whereabouts in Essex you are (roughly). You've been messed around so much that someone might offer to help, as the diagnosis should be a quick job.