This post is 4½ years old, it is unlikely you will get an answer from original poster of the thread. So if you have 4 storage heaters of 1 kW each it is likely they all run together so 4 kW for heating, if you have 24 storage heaters than 24 kW for heating simple maths, then you add for other house hold use, and between 11 pm and 6 am that will not be much, so likely 3 kW will be enough, however I have not seen a DNO fuse under 60 amp, so likely it will be 4 x 60A supplies.
However you will note the question was asked on how people in flats would be billed, and this was never answered, in my home we have main house and flat below it, whole lot only has a 60 amp supply.