If the system has been properly designed, with a well insulated cylinder of an adequate size, and you are on a tariff where there is a considerable difference between the off peak and peak prices for electricity, then it will be much more expensive to heat the water constantly.
If one or more of the above hasn't been met, then the difference in cost will be less.
How many immersion heaters are there on your cylinder? If there are two, it may be that the lower one isn't in use, and you are only heating part of the cylinder at night.
Do any of your hot water pipes run underneath a downstairs floor? I had a case once where there was a leak from the hot water pipe under the kitchen floor , in the pipe to the sink hot tap, and all the hot water was gone within a couple of hours after the heater was switched off.