Slow overflow - possibly from hot water cylinder

[motorbiking]

I didn't fully understand the logic behind some of the replies so, I'll offer my interpretation...

1) For many months there has been a slow trickle of water out of an overflow pipe onto the flat roof below. It feels warm, but not obviously hot, and I'm not sure which part of the system this overflow come from.
2) I recently replaced a (wrongly specified) shower pump with a proper negative head one, which now activates as it should, except it also kicks in for a second or so every half hour, as if there is a leak in the system.
3) The feeder cistern above keeps filling (float valve never quite closes), but it does not reach the overflow.
4) the vent pipe from the cylinder up to the cistern is hot to touch.

1 - you might have air in the closed loop system, you might also have your circulation pump set too high or low: change the pump speed, consider adding a bit of inhibitor and Try bleeding all your radiators and consider flushing the system and adding new inhibitor.
2. - you probably have a dripping shower or some air in the system
3 - leak or drip somewhere as others have said, but it might be that when the hot water is on and the water expanded - it does reach the overflow. Is this an expansion/vent tank?
4 - yep because the hot water is expanding and running up to the expansion tank.

This might be nothing more than adjusting the ball valve so the tank is less full, bleeding all the radiators, turning the pump down so that the air can get out more easily