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Some fungi are very poisonous so a mistaken ID could have serious consequences.
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It has white particles on the stem, I don't know if that is a useful diagnostic characteristic or not but does seem a bit unusual.
actually just come across another little white mycena http://www.ispot.org.uk/node/292099 which might be more like m. galopus as its a bit more meaty than this one.
I am wondering if the current observation might be towards m. lactea or one of the other smaller ones rather than galopus which i always think of as a bit more sturdy with thicker stem.
If a drop of Meltzers on the cut gills turns them red/brown - Mycena if not Hemimycena (lactea) is probably a better suggestion. The white particles are the Caulocystidia and they are much more pronounced in H lactea.
Lat/Lng: 51.946379, -0.67698277777778
OS grid ref: SP910283