If you have storage heaters you usually also have an immersion heater for hot water connected to the interruptible supply in order to take advantage of the much lower price of electricity.
This Page describes a very simple vented system, the sort we have had for forty years. Whether you heat the water by gas or electricity a vented system needs a cold water tank, often in an attic but anywhere higher than the hot water cylinder will do, even immediately over the hot water cylinder in the same cupboard. If you do not have a cold water tank you can use a non-vented system - this works in almost exactly the same way but is more complicated and expensive to install and maintain. The differences between vented and non-vented systems and the advantages and disadvantages of each are described on other web sites.
A non-vented system produces a higher hot water pressure than a vented system, but it is simple and inexpensive to add a booster pump to a vented system if you need to, for example for the shower, and this is what we have done.
To take full advantage of interruptible electricity, whether you have a vented or non-vented system, you need a well-insulated cylinder big enough to store enough hot water for the whole family for the whole day. Suitable cylinders come with holes for two immersion heaters, one at the bottom to heat all of the water in the tank, and the other near the top to heat just the water at the top of the tank. (Hot water rises, so when only this heater is turned on the water below it does not get even warm.) The lower heater is connected to the interruptible supply, and the upper to the ordinary supply, to give a small amount of hot water quickly at times when the lower heater has not been turned on for a few days (for example when you get back from a holiday), or if you run out of hot water before the end of the day. (Even when we had three teenage children at home this almost never happened to us.)
A thermostat on each of the heating elements turns it off when the water has reached the right temperature.
There is just one small problem, easily overcome. If you forget to turn the top heater off after you have turned on the lower heater you will be using the top heater unnecessarily and be paying for the electricity used by it at the full price not the interruptible price. To overcome this problem it is best to fit the top heater with a timer so that it turns itself off after, say, thirty minutes, or to have a warning light in a highly visible place, or of course both.
All hot water systems are affected by limescale in hard water areas but immersion heaters more than gas boilers. If you have an immersion heater (and remember there are immersion heaters in your dishwasher and washing machine) you really ought to have a water softener. It will pay for itself in quite a short time because you will save money on detergents and water softening tablets (or repair bills!) for your dishwasher and washing machine, and of course having a bath or shower will be a lot more pleasant.