Small fungus with a cone-shaped cap.
Caution: Do NOT use iSpot to identify fungi to eat!
Some fungi are very poisonous so a mistaken ID could have serious consequences.
No interactions present.
Good set of photos showing lots of detail. Unfortunately in this case there are a few arboreal Mycena that look very similar so it would need a microscope to take it to species. Did you notice any aroma?
I didn't notice any aroma. But I didn't give it a really good sniff; I'm new at fungi and could just about ID a Fly Agaric or say "look, a bracket." I'll be taking a notebook with me in future and I have Roger Phillips' book and access to his web site ...
With that set of photos you are off to a good start.
Lat/Lng: 51.3868, 0.0292
OS grid ref: TQ412672