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Which one are you after an ID for...the grass or the purple flowers?
My Flickr photos...
The grass, but now I've looked back at them I don't think the 2 pictures are of the same plant. I uploaded them thinking they were, so perhaps there are THREE different things here! Feel free to ID all of them if you know what they are. Thanks in anticipation.
The inflorescence shape, tufted habit and habitat all point out to D. cespitosa but it is difficult to be sure from those pictures. You can identify this species confidently in the field even vegetatively through the winter by running your fingers along its leaves (it is extremely rough) and by holding the leaves against light (very clear stripes). Good luck
Lat/Lng: 54.0897, -0.8365
OS grid ref: SE762666
Yorkshire wildlife trust nature reserve.