The structure on the oak nut is a knopper gall.
> It is a distortion of growing acorns on pedunculate oak (Quercus robur L.) trees, caused by gall wasps( _Andricus quercuscalicis_ ), which lay eggs in buds with their ovipositor.
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An _Andricus quercuscalicis_ larva in an open gall of an acorn: Link
Here's a video by BBC on the same you may find it interesting.