I 'think' they are galls in which case they have a wee beastie inside them.

So they're harmful to the tree, Moon grower ?
I've not seen this before :-/

If it is a gall it won harm the plant - just not sure this is what it is... It isn't beech seed!

dont think they are galls, usually in the leaf not hanging from it, can you check if the fruit has a stone, and are you sure it is a beech tree.

Rob,

As Steve suspected your tree is not a Beech - the leaves are the wrong shape and colour - it's an ornamental Prunus, and those are it's fruits....it would have flowered, (though possibly not very prolifically or noticeably) at some point during spring too.