These photos were taken on 6th January. This was growing in my new garden in Swindon out of a bit of sacking that turned out to be hiding a tree stump. I don't know why you'd want to hide a tree-stump, perhaps stumps are health hazards or something, but anyway this rather gives the game away. The caps were as shiny as jellyfish.
I think it is the edible mushroom Velvet Shank (Flammulina velutipes) . According to this excellent site, Velvet Shank grows during warm spells in winter. Our winter has been nothing but one long warm spell so far, so that would figure.
But all I'm going on is the unusual date plus the dark stems and uncrowded gills and slimy cap and a general resemblance to other internet pix of F. velutipes. I'm totally not a mushroom expert so if you think it's something else please tell me!
Facebook consensus is that I've got the ID right. Here's another good article (definitely a site to bookmark if you interested in wild food) :