There are several different off-peak tariffs available, but Economy 7 is the most common, so named because it provides power at a cheaper rate for 7 hours each night (normally midnight to 7 a.m. GMT, but sometimes there can be a half hour variation either way).
Storage heaters should be wired to a separate electrical distribution panel, which has power turned on only during the off-peak period. So you can leave the wall switches for those on throughout the period of the year that you need heat, since the elements will only be running when the timeswitch cuts in at around midnight (or 1 a.m. during BST).
Electrical water heating with Economy 7 can have several different arrangements. Sometimes there is a single element, and the system is powered from the 24-hour supply, but through its own timer so that it can be set to come on overnight during the off-peak period to provide you with a cylinder full of hot water in the morning. You can also set the timer to give a short boost during the day (typically late afternoon) at the normal rate. There will normally be some sort of manual override to let you boost the water at any time (sometimes just switched on & off completely manually, sometimes a boost button which gives an hour or so and then automatically switches off again).
In some Economy 7 heating systems the water cylinder has two elements, one wired to the off-peak supply the same as the storage heaters so that it comes on automatically at the correct times, the other wired through a switch to the regular 24-hour supply to provide you with a manual boost.
There are two or three other variants which can be found, so we'd need to know more about the particular system to be specific.
The other tariffs provide different rates and times (e.g. Economy 10 is basically Economy 7 plus another 3 hours at reduced rates during the day), but the basic principle is broadly similar.
