Hag stones, or 'mare stanes' in Scotland - have a looksie
here 
They're easiest to find around running water, beaches and streams and the like, but you also find them where there's a lot of flint. We get loads of them turning up here as the Chilterns have large quantities of flint lying around from the old chalk pits hereabouts.
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I don't think it counts if the hole has been made by water i.e - you can't get them from the beach
Never heard that before. One of the reasons that hagstones are considered protective is the old belief that you can't 'magic' running water. Hagstones, usually found in streams, were therefore considered to retain the protective qualities of the running water.
Hagstones have been credited with curing stomach aches (protecting against the hag that sat on the stomach of the sick man/woman and caused the pain), protecting animals in stables (the stones being strung above the door), preventing milk from curdling in thunderstorms if kept in the dairy (by protecting against the evil spirits who are most active in stormy weather), preventing nightmares if suspended over the head of the bed, and protecting ships at sea if attached to the prow.
There was also a belief that if you looked through the hole in a hagstone, you would see what was 'truly' there and thus be able to dispel glamours used by fairies in order to mislead you.