All electric heaters are equally efficient at converting heat into electricity. Having said that, if you use very little hot water, you may find you would use less electricity by using electric showers and/or a small point-of-use electric water heater rather than heating a whole cylinder and having it slowly go cold over the day. Though if your house is also heated electrically, you will probably only notice the difference in the summer months as the heat lost from that cylinder is currently heating your flat.
Also bear in mind having economy 7 is a mixed blessing, because you pay less for night rate and then they charge you more for the day rate units.
If you are on a pre-payment meter, contact the electricity supplier Ebico and see what they are charging, as they used to be one of the cheapest for this payment method.