Seen near the pools between conkers and spring cottage with otherwise mostly white examples but the pink shade seems to suggest the brittle gill
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With fungi, it's always…
With fungi, it's always helpful to have pictures of the cap and detailed pictures of the gills and stem for identification. A slightly wider shot of the environment they were growing in can be helpful too.
Assuming it was growing under Birch trees, it could be, but the britlegills are notoriously difficult to identify - you need to examine the spores under the microscope.