Having a similar problem. (overflow pipe dripping out onto outside of property, only unfortunately, onto the street and in this cold weather, it is freezing and if someone slips over, I reckon they'll have me over a barrel!)
I suspect faulty washer in valve as it drips from that area of valve/arm - but in the smaller of the 2 loft tanks.
So, does this mean this is the tank for the radiators, as I have read? (Because when I pushed down on the ball cock to let water come in, water was warm?!...) And if so, would turning off the water from the main stopcock (which in my house is not under the sink in kitchen as I thought, but inside my living room carpet of all places!) not work?
I turned off all red round valves I could find in my sons room which is where the boiler is. One on the cold pipe (runs straight up sons wall - floor through to ceiling - bypassing the boiler system altogether, I think) and one pipe which was warm, just underneath the heating pump. Even when turned off both of these pipes, the smaller tank up in loft was still drawing water from somewhere (whcih was then cold?)
Just don't want to relish turning living room upside down to get to main stopcock to turn off supply if I can help it...
Sorry for hijacking / resurection a presumably old thread - google brought me here
Sarah