Thank you very much for these very good suggestions. Based on some initial googling, I believe that a combination of these tips may solve the mystery.

lannerman and Jeff: the Clematis armandii and the Viburnum tinus both look like what I imagined as I read this chapter.

Janet: I believe the Hawthorn story may offer the best clue yet! I had left out a detail of the story - as the main character accepts a flower, he is inadvertantly jabbed by a pin attached to the flower. Because it was a pin, not a thorn, that caused the injury, I didn't think this was important to the botanical mystery, but it may be Gaiman's updated hint that the plant is (symbolically, at least) a thorn. Acting on your suggestion, I also came upon this interesting article, "The Holy Thorn Ceremony: revival, rivalry and civil religion in Glastonbury," by Marion Bowman.
http://findarticles.com/p/articles/m.../ai_n16676590/
After reading only one page, I can see that it matches many of the details of Gaiman's fictional "local tradition" and probably served as an inspiration for the Danse Macabre chapter.

Thank you all SO much! I am so grateful for your excellent input.
- Sara Hathaway
(now in the Berkshires in New England, but only thirteen generations removed from the Forest of Dean)