Bonnet fungi
(Mycena species)
There are over 100 species of bonnet in the UK and many cannot be accurately distinguished without expert microscopic examination. For most of us non-experts, it's maybe enough to identify that we have found a Mycena species rather than another similar small fungus.
Features of all Mycena are a fragile stem and a cap that starts almost conical, progressing to bell/bonnet shape, and flattening as it ages. If you'd like to take a spore print, they all have white spores, so take a cap and leave spore-side down on black/dark paper.