At last, a fungus identification that we can be confident of! This one’s unmistakable (if we ignore a few rare relatives), its the Magpie Inkcap (Coprinopsis picacea). It doesn’t look good to eat and it isn’t – its poisonous.
The Collins Complete Guide says it’s relatively rare but most often found with Beech on Calcareous soil – exactly where ours is. We’ve never noticed them before but today there were maybe a dozen around our oldest Beech tree, standing alone and mostly in various states of decay. They go from the pristine youthfulness above through the ‘dripping edges’ phase just starting in the specimen below and then to an unappetising black blob of slime – often in the same day. First-Nature says this (deliquesce) is a process which aids spore dispersal particularly in wet weather.