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I don't know what species either common or marsh buttercup refers to.
It's not celery-leaved buttercup (Ranunculus sceleratus), which is the buttercup (as opposed to spearwort or crowfoot) most associated with marshes. It's not bulbous buttercup (Ranunculus bulbosus).
A view of the foliage would probably settle the identification. From the structure of the flowering shoot I would go for meadow buttercup (Ranunculus acris) rather than creeping buttercup (Ranunculus repens). Ranunculus repens is the commonest buttercup (at least around here); it is also more likely to be found in flooded ground than Ranunculus acris.
PS: you probably meant Ranunculus sp.
Lat/Lng: 51.8774, -2.089
OS grid ref: SO939198