if you can loosen the belts and pull the sectional jacket off, we can see the cylinder better. You can put the jacket back after taking the photo. But it looks to me like a direct one (this suggests you do not have a gas boiler) which is cheaper and more simple to fit than the other kind.
As you have Economy 7 you can (and most people do) have the bottom immersion heater run off the E7 supply, often with a 24-hour supply to another heater near the top for topping-up at full price if necessary. In this case it is a great advantage to have the cylinder very well insulated. new cylinders come with plastic foam coating applied at the factory, but you can put a red jacket over the top and lag all the pipes if you like (I do) as well, and it will easily stay hot for 24 hours (unless you use it all sooner).
I would hope that, as you have E7, the immersion heater is already connected to that supply. If the E7 supply automatically turns off during the day at the meter, you do not need another timer.
E7 electricity is about half the price of daytime electricity.
If you post pics of your electricity meter(s), consumer units (fuseboxes) and the various cables between them, we may be able to identify how it has been done. You can post this in the Electrics UK (not the plumbing) forum.