There is a constant dribbling of water into my toilet pan making an annoying dripping noise. My toilet was fitted just over a year ago and the cistern comprises a plunger operated from a button on top of the cistern and another device apparently controlling the water input (I know nothing about such things!). There is no water entering the overflow into the pan as the filled water level is about 2cm below it. Any ideas?

This could be a leaking flush valve, the thing you activate when you press the button or it could be a leak around the bolts that hold the cistern to the pan.
If it is the flush valve leaking you should not hear a dripping noise as the water should flow down the sides of the pan. But you should also hear the cistern being refilled periodically.
A leak around the bolts between he cistern and the pan could be putting water on the top surface of the pan which could then drip into the pan creating the sound of dripping water. Dry the surface between the cistern and the pan. Place tissue in that area to see if water appears. Or put some food colouring in the cistern to make the leak more visible. If the leak is around the bolts, correction may be to just tighten the bolt slightly. Be careful not to over tighten and break the cistern. It may be necessary to remove the bolts, add some sealant under the head of the bolt and reinstall.

Thanks for that. Strangely, the problem has stopped, although it has done that before. I suspect it is not loose bolts as there was no sign of dampness between the cistern and the bowl. Anyway, I am sure the water was coming from under the bowl rim. If it is a faulty flush valve what's the cure?

Flush valves can be cleaned or rebuilt but replacemnet is usual only $9. If it leaked and stopped, it will start again. Make your repair and/or re[placemnet at your convenience even if the leak has not started again, it will.