storage heaters must have good air circulation, or they will overheat and the internal thermal fuse will melt.
So a shelf a couple of feet above will be OK,, but nothing on top of the heaters. People who drape wet washing are bad for this. There will be finbe black dust marks rising from the heater.
If the immersion heater was "bubbling" then it probably has a failed thermostat which is dangerous as the water may be scalding or boil and may melt the cold water storage tank above if it is plastic. Changing the thermostat is an easy plumbers job. More modern thermostats have a safety cut-out to turn then off if they overheat.
If the home has an economy 7 type tariff, then there is probably (should be) a timer-controlled immersion heater near the bottom of the cylinder, and a full-price top-up element near the top, to be manually switched on if you have used all the stored water and need a bit extra during the day. Thsi should normally be switched off, but get that thermostat changed anyway. Scalding is a particular danger with small children and with aged or infirm people. The cylinder should be very well insulated so it will keep water hot all day at low cost. What colour is it? (this is not a joke)
Look at the electric meter. It should display Cheap Rate and Day Rate usage separately. You might have to push some buttons. Write both the readings on the calendar at least monthly. The electricity co will have "how to read your meter" on their website. The daytime usage should be very low as it will mostly be running lights, TV, cooker. The nighttime should be higher as it should be running hot water, and storage heaters in winter. Storage heaters are hottest in the morning and run out of power by evening, so buy mum an electric blanket, and possiblly a small, oil-filled electric radiator for the bedroom. Oil-filled are not a fire risk like most electric heaters as they have no red-hot element inside and the casing does not get hot enough to burn you. They can be fixed to the wall to avoid being knocked over. They all have thermostats these days but a timeswitch will help for economy. Only a 500W heater should be needed if it is in the bedroom, and during the night it wil probably run at cheap rate most of the time.