Finally some fungi I can identify with confidence because, as Pat O’Reilly explains on the First Nature website,

Cap colour is rarely of much help when you are struggling to identify a Mycena, as they vary so much with age, location, humidity and growing substrate. If you look closely at the stem of a Grooved Bonnet you will see that it has longitudinal striations, whereas other common bonnet mushrooms have smooth stems.

So, the striated stems you can, hopefully, see in my second photo below prove that these lovely little bonnets I found growing in a tree in the grounds of a local church are … taaa daaa! … Grooved bonnets (Mycena polygramma).