Cold water tank overflow pipe problem

We have had a leaking overflow pipe coming from our roof of our house. The plumber has been twice and has changed the two ballcock value in both tanks but it han't solved the problem. Any ideas?

I thought for a moment that you were talking about a toilet but is this a cold water storage tank in your attic? If so, can you see into the tank to tell if the ballcock is actually closing?

What is the cold water tank for

I am guessing that in some courties, UK for example, there frequently is low water pressure so water is slowly filling a tank in the highest part of the home. Gravity then provides a slightly increased water pressure below.