It probably depends on the type of heating you have, and just how cold the weather is too.
We have an air source heat pump.
If it is on for the heating, it heats the water too. There is no obvious way of having one without the other, and the system is designed to be turned on all the time.
For a couple of months at the end of last year, we were having big problems with the heating part of it - it was out of control, randomly heating the house far too much, no matter how low the thermostat was set..
Because of the problem, not wanting our energy bill to soar, we turned the whole system off, and only turned it on for up to two hours morning and evening, largely so we would have hot water.
(We still have an open fire in our living room, so I gathered fallen branches to burn on that in the evenings when necessary, though luckily the weather was relatively mild for the time of year anyway).
I was reading the meter every day, and quickly discovered that we used as much electricity doing that as we usually did by leaving the system running 24/7!