The first step is to get into the loft (strip first, in this heat), and see whether or not water is dripping from the ball valve when it should be shutting off.
If it is, then the solution is really simple - replace the ball valve. They can be repaired, if you reeelly want to, but they're only a few quid and it takes only a few minutes to change one. Tip - don't remove the whole assembly from the cistern, just undo the . Clearly you need to shut off the mains while your doing all this.
If there's no drip from the ball valve, then feel the temperature of the water. If it feels warm, then I would go looking for a shower valve that has mains-fed cold and tank-fed hot supplies. This imbalance has been known to cause cold water, at mains pressure, to force stored hot water from the cylinder up to the cold storage cistern. The solution is rather more complicated, because you need to balance the pressures to the shower valve.
The same thing can happen to a basin mixer; not that I've seen it happen, but others on the forum have reported it.
Hope that helps.