Candlesnuff Fungus (Xylaria hypoxylon) is one of the most common fungi in our woodlands, usually growing on the wood of broadleaved (non-conifer) species.
White Fibrecap (Inocybe geophylla) is a small, poisonous species which often grows in groups. It also comes in a beautiful lilac form, now regarded as a separate species (Inocybe lilacina), which is common in Gower woodlands.
Lepiota pseudolilacea is a type of Dapperling (it doesn't have a common name that I know of). It usually grows at the edges of the forest. It is similar to the Stinking Daperling (Lepiota cristata), which is much more common and differs in having a strong, unpleasant smell.
The Webcaps (Cortinarius) are a very large group of species, with over 100 species in Britain. Variable Webcap (Cortinarius anomalus) is one of the more common representatives. The young gills usually have a violet tint. In the photograph you can see the cobweb like veil which covers the gills before the cap expands. This veil is called a cortina, and is a feature of this group of fungi. Hence the name, Cortinarius. In older specimens the cortina disappears and the gills become dark brown in colour due to the production of brown spores. As the common name suggests, this is a very variable species and may in fact be a collection of similar species. It often grows with birch at the edges of conifer forests. If you walk or bike along the forestry roads, your bound to see it sooner or later.