If I understand you:
You have a working spring loaded one way valve (a proper check valve, airtight, not a flap valve that is only ish) on the cold distributing pipe, so we can rule out problems with mixer taps backfeeding up the cold distributing pipe.
You have a similar valve on the cold feed to DHW cylinder, then that rules out split coil and mixer taps passing water back up the cold feed.
The water can now only get into the cylinder from the top: the vent and the fill valve. Since the vent is only allowing a few drops of water through, we can assume that is normal expansion of water and not a punctured coil or mixer issue causing backfeeding through the DHW cylinder and vent pipe.
At this point, either you have a very leaky roof, or the water is coming in through the ballcock, impossible as it may seem.
Do I understand correctly, Terry?
If so, at this point, use a 15mm blanking cap on the tap connector that normally goes onto the ballcock and, if the level of the water does not rise overnight, I'm right, as by capping the ballcock, you aren't affecting anything else. If the level still rises, I'm missing something.
Final thought: is the overflow shared with something else and the cistern is filling through the overflow?