Sedge, Rush or Grass?

Large areas of the local woodland floor, and the shady banks of some of the damper-sided lanes, are carpeted by this plant. Such is the depth of my ignorance that I'm not sure whether it's a rush, a sedge or a grass, which makes identification - which is something I am always driven to attempt - rather more difficult.

I suspected that this might be a rush, and the internet tells me that there are only 32 species of British rush or wood-rush, so I felt I should be able to identify it. 

It has distinctive characteristics. The plant has a fairly broad but elongate leaf, is about 400mm high, and the flowering part divides and divides again. About as close as I could get to it was the sharp-flowered rush, Juncus acutiflorus, or the blunt-flowered rush, Juncus subnodulosus.

However, I'm now fairly certain it's great wood-rush, Luzula sylvatica, the largest British rush, which is described as favouring woodland and damp, shady places.

It and the other plant that covers the forest floor - the bluebell - seem to be pretty exclusive: you either have the one or the other.