Fontburn in Northumberland is smack bang on one I think. But It's more of a weird kind of cairn than a proper circle. However, just to tickle one of your cherished theories, there is an unexcavated hengiform enclosure on the other side of the steam there, and another a couple of miles south.

According to The Denham Tracts, cattle on the Nbland sections of the cross border drove roads were driven twixt two bonfires ( on either equinoxes, solstices or both, I can't recall) up until the back end of the 18thC.