Approx 10 cm in height, slender stem, pleated gills.
Caution: Do NOT use iSpot to identify fungi to eat!
Some fungi are very poisonous so a mistaken ID could have serious consequences.
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Thanks, having looked at the images for other observations, and a Google image search for Laccaria proxima, this looks like a very good match.
One source suggested that proxima only grows in pine forests, which this site definitley isn't. Another suggested that proxima could be found on moorland though.
If this is Laccaria proxima, it is in a square not currently recorded in the NBN map.
Maybe L. laccata? MushroomExpert.com says "Separating this species from the very similar Laccaria laccata requires a microscope; both species are variable enough in their macrofeatures that the differences visible to the naked eye are not definitive."
Lat/Lng: 53.857171514255, -1.7720174789429
OS grid ref: SE150401
Edge of the moor, amongst sedges and grasses and some small rowan and birch saplings.