Instead, having done some online research I decreed that we would take the tap to pieces and attempt to identify the broken bit.
I turned off the water! I drained out the water! I looked carefully at the tap and worked out what tools to use! I learned which bits are the ceramic tap glands and removed one of them (Pp, encouraged by my success removed the other one). I sourced new ceramic tap glands of the correct size and model and ordered them, while Pp, still feeling encouraged, put the old tap parts back together temporarily! I turned the water back on, and the kitchen did not impersonate a fountain and leap on high!
The tap no longer drips. I can't decide if I am pleased or annoyed about this, but at least we have a non-dripping tap, a spare set of ceramic tap glands, and a feeling of having Achieved Something.