Check the motorised valve feeding the cylinder (the metal square box) is it jammed?, is there a power supply problem? if you select hot water it should take about 20 odd seconds to open and about half that to close. If the motor has gone you can buy a new one for about £20 and there easy to fit. Just remember to isolate the electric supply first. Also check your thermostats, sounds like the low level one is ok but you have
a second one higher up the tank and poss on boiler as well, keep us posted and dont neglect this as unvented systems can under certain circumstances be dangerous. Good luck!