Probably the off-peak meter has a timer to turn the immersion and storage heaters on during the night.
Your hot water cylinder might have got two switches, one for off-peak and one for daytime (only to be used for top-ups if the hot water runs out). There is probably a separate timer. It may have a radio-controlled switch or a clock in it.
What colour is the cylinder? This is important. Photos of the wiring and switches around it will help.
Ask your electricity supply for the details of your tariff. You want to know the hours and the prices per kWh and the standing charge.
You can change to another supplier if they have a better price or hours.
Avoid prepayment meters if you possibly can.
In your meters, there is a horizontal spinning disk. The faster it spins, the more electricity is going through that meter. By turning the immersion heater switch(es) on and off you can see which meter is being used at various times.
Input your meter readings online every month for accurate bills, and keep a separate note in a diary or calender (note the weather and any changes to settings).
If you are at home all day, and are elderly or have small children, and go to bed early, storage heaters are not too bad. If you are out all day, they will warm your home while it is empty, and run cold by evening.
Your heaters probably have knobs or switches to adjust input high/low (controls electricity used to get them hot) and output high/low (controls how fast they emit the heat and go cold). Try setting both to low and see if that keeps your home adequately warm.
If you can run appliances such as a tumble drier, washer, dishwasher during your off-peak hours it will be good value. Tumble driers in particular should not be run unattended in case they catch fire.
I presume you are in a rented flat with no gas, otherwise you would probably not have storage heaters. Next time you move, avoid them. Do not drape towels or washing on top or they will overheat.