On the plus side, I found some more, BIGGER, fungi.
Having learnt my lesson from yesterday, I did bring a specimen home: It doesn't look particularly downy. But then it doesn't look particularly young either.
In conclusion: it's probably either Coprinus micaceus or C. truncorum, with C. micaceus being the most common. Except I don't think they're even called that any more. I tried Googling them to find out if there's a way to separate these two species without a microscope and discovered another name for this genus is Coprinellus. Looks like Coprinellus is is the preferred name, according to the British Mycological Society GB Checklist of Fungal Names.
So, either Coprinellus micaceus or C. truncorum then.
For the record
Location: Horton Wood, Small Dole
Grid reference: TQ208127 (site centroid)