I suspect the additional rings are probably faery rings. I walked along the linear feature to the escarpment edge and didn't see anything, all though it was quite a while ago and I do have a certain rep for missing things that are right under my nose (eh Rich?).

"though something tangental to a circle is perhaps better described as a row"
This is definitely not a row it is a bank, if bank is not acceptable then it is a low, narrow, continuous linear earthwork, constructed of earth and small stones.
The NYMNPA seems to think the bank could be part of an enclosed cemetery, which would kinda fit in with the monuments.

It's an interesting area, paleolithic remains have been found in the area, there is a circle on the moor above, a henge on the opposite side of the valley as well as a great cairn and bits and bobs of rock art. The lead mines that honeycomb the nearby rock face are fantastic too.