Help!

The ball-valve on my cold water tank never completely closes, so water is constantly running into the tank. The tank should logically overflow because the water does not stop completely, but it doesn't.

I have replaced the ball valve and the problem still exists. Turns out the cold water tank is losing water continually, but I have no idea where it is going too or why. I can only assume a leak.

I turned the stop tap off over-night and during the night, almost an entire tank of water dissappeared even though no water was used.

Any ideas what's going wrong please?

I'm going to take a guess and assume that you're talking about the toilet tank.
Run your finger around the flat part of the flapper. If it's wavy or has rough spots replace it. It certainly sounds like it's bad. My bet's that's where your lost water's going. Regards, Tom