Nicole: Thank you for your last post. You are clearly exasperated and who wouldn't be. I'll explain what I think is the situation at the moment.
1. Your flat relies on electricity for space and water heating. To be most economic you need to be on a dual rate electricity tariff such as Economy 7 or Economy 10. These provide periods of cheaper rate electricity. Time switches are used to turn the space heating and water heating on and off to utilise the cheaper rate periods. At the moment you do not have a dual rate tariff. I believe you 'lost' a dual rate tariff when you swapped from the pre-payment meter to a credit meter with British Gas.
2. Your hot water tank has two elements, the bottom one to use cheaper rate electricity and the top one as a boost using whatever tariff is operating when it is on. What I cannot know now is whether the time switch to the left of the Delta Dore controller was for the bottom element to switch it on during cheap rate; the top element being then simply controlled manually by the left hand 'Water Heater' switch - you'd have to remember to turn it on and off.
3. I reckon though that the time switch to the left of the Delta Dore is for the top element as it is used now. The bottom element was then being switched on and off for the cheap rate by the old prepayment meter. There is a hint to this set up by the thinner brown grey vertical wire going into the brown plastic box with 'PROTEUS' written on it. I believe it previously went into your old prepayment meter. But since your change to a credit meter, which does not have an output which switches on and off during cheap rate, it has been connected to the brown box which now provides a permanently on supply for the bottom element. The bottom element is now only being controlled manually by the right hand 'Night Immersion Heater' switch. Thus, the change from prepayment to credit meter has resulted in no time control of the bottom element meaning it has been on constantly albeit regulated in temperature by its thermostat. Meter change men/women are not obliged to ensure any downstream effects of the meter change are attended to. So since your meter change I believe - perhaps you can confirm from experience - the top element has been controlled on/off by the time switch left of the Delta Dora and the bottom element has been on permanently if its switch is on.
4. Now, I may not have the full history of this panel correct because one can see a square white plastic blank fitting bottom left below the 'Immersion Heater' switch. It may have once had a square timer here which looks like this:
Electrisaver Immersion Heater Booster - https://www.tlc-direct.co.uk/Main_Index/Water_Heating_Index/Immersion_Heater_Timers_2/index.html
or this
24 Hour GP/Immersion Heater Timeswitch - Flush/Surface | Timeguard (NTT01) - https://www.tlc-direct.co.uk/Products/SMNTT01.html
These would control the top element. The timer to the left of the Delta Dora would then do the bottom element.
5. With me so far? ;-)
6. Good. You told me that you had never seen the right hand 'Night Immersion Heater' switch orange light on when the switch is on. This is odd because now, since the credit meter, it has a permanent supply all day long via the red switch and the 16A circuit breaker on the far right of the consumer unit and it is clear from the photo that these two switches are both on - they in the up position. This indicates that the supply has been disconnected somewhere at or before the 'Night Immersion Heater' switch. This begs the question why would someone do this?
7. I suspect - cannot know for certain - the plumber has disconnected the supply to the bottom element because he found it defective. The spare on order would be the replacement element. He may have temporarily connected the top element to the timer to the left of the Delta Dora to the top element or it may have been always so.
8. I cannot investigate the disconnected supply because it would require live electrical equipment to be opened up. This is why I said we must wait for the plumber to return and finish his work and I asked you to clarify with him how the top and bottom elements have been connected.
9. When we have two working elements we can discuss dual rate tariffs which depending on your lifestyle and electricity use profile may be more economical. You could have a read of these in the meantime from which you will learn about E7 and E10 and some other tariffs.
What is an Economy 7 meter? | Understanding Economy 7 - https://www.uswitch.com/gas-electricity/guides/economy-7/
What is Economy 10? A complete guide to Economy 10 meters and tariffs - https://www.uswitch.com/gas-electricity/guides/economy-10/
7 facts about Economy 7 meters, tariff and times - https://www.edfenergy.com/energywise/all-you-need-know-about-economy-7
10. I hope this provides some clarification. The most important thing to say is that as a tenant your landlord is responsible for fixing this problem in a timely fashion using qualified contractors. It is reasonable to wait say a week maybe two weeks at most for spare parts but any longer it is not. How long ago since the plumber visited?
11. I have sent you my mobile number if you want to call me. If I don't answer straight away leave a message or send me a text/whatsapp.
PS: Re your #6 - it looks like the top element white wire goes into the timer and the bottom element white wire goes into the white plastic trunking - is this still the case?