As you are keeping us guessing as to what the overflow serves I will guess a solution.
My guess is the mains stopvalve hasn't fully turned off the water [possible worn washer] and the cold water tank in the loft /attic is still being trickle filled because the washer on the tank inlet valve is also worn and not shutting the water off. Check the tank see if it's full. If an overflow leaks even a bit it must be being fed from somewhere. Post the solution if you reach one.
Nobby, February 2009
