Water tank(s) in loft

[mrmikelucas]

Hi all , I have recently brought a new house - I keep getting a drip from the water overflow. I have inspected and found two tanks in the loft, a small one and a larger one next to and below it .
The larger tank was full , almost to the top. The water level was above the ballcock, I changed the Ball and it hasn’t fixed.
From what I can tell there is no leaks drips from the valve its self ...
1) what are the two tanks
2) how and why does it fill up past the ballcock
3) is the valve faulty

 

[Ian H]

Is it a brass one? You might need to bend the arm to lower the ball.

 

[John D v2.0]

1 small is for heating expending and large is for cold water storage before it goes into the hot water cylinder.
2 mustn't be shutting off, maybe needs a new washer or adjusting as per Ian h. Presume that's the one overflowing right?
3 could well be

 

[dilalio]

Probably got a bit of grit come through the rising main and now caught in the ball valve stopping it from shutting off.
Might as well change the valve while you’re up there