the small tank is likely to be the feed & expansion for your central heating and boiler.
I expect it has a ball valve in it, like you find in a toilet cistern.
First, check the depth of water when the system is cold. It only needs to be a couple of inches above the outlet at the bottom (to allow for expansion). You can adjust the ball valve; if a plastic one, with an adjusting screw near the pivot; if a brass one, by repositioning the ball on the bend at the end, or by bending the brass arm.
Second, look in this small tank and see if it has a layer of fine rust sludge at the bottom
and bleed your radiators to see if they contain gas
and black water
or sediment
If so, the overflow may be caused by corrosion of the radiators which generates gas, which displaces a volume of water, that can only escape into the F&E.
Also, look at the water level in the large tank that supplies your bath taps via the hot water cylinder. Compare the height of the water level in this tank with the height of the water level in the small F&E. I don't mean the depth of water, I mean the height of the top of the water relative to the loft floor (or, height above the ground).
Please come back and report what you find.
Has the central heating system ever been flushed or cleaned or filled with inhibitor? How old is it?