It suggests you have a gravity fed system, the water tank should have a lid as you will naturally get condensation from having a open water tank, it also stops contaminants getting into the water (eg something dropping into the tank), this would normally cause mould and condensation in and around the cupboard not the entire flat though.
You can buy a generic lid to fix on it from tool station here, another cause of increase humidity is if the hot water tank is over heating as you will find as water expands in the tank it can overflow into the cold water tank, which can cause increased condensation but not enough to heat up the water in the tank itself for you to notice.
My suggestion would be check if the hot water tank is overflowing into the cold water tank, it should be a copper pipe which sits over the tank, turn the hot water on give it an hour then go and feel the pipe if its hot it suggests its overflowing into the tank, and the thermostat in your tank needs replacing.
Secondly get a lid for the tank, it will benefit you as much as her, as you dont want contaminants getting into your drinking water.
Lastly if the cupboard is on an outside wall suggest she gets a external vent fitted to increase circulation, this is what the council would recommend on any property with damp\mould problems, and should be at her cost, depending on where you live it would be around £100.