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At the time of writing, Carex paniculata is still shown as the likely ID. It is not that species, which in any case is rare in East Lothian.
C. otrubae, as shown here, has more spreading beaks to the fruits, occurs in much smaller tussocks, and is frequent on the East Lothian coast.
... (here I see Carex otrubae mainly as tufted plants on canal margins) but on looking a the plants again I agree that they are Carex otrubae. I'm not sure what I was thinking two years ago, but I likely interpreted them as young plants of Carex paniculata.
Two years is a long time!
Lat/Lng: 55.9711, -2.4234
OS grid ref: NT736754