At least in South West Britain and Cornwall, hunting the wren is a long faded memory basically. The point was that it’s strange, even paradoxical, given that an old adage goes that “he who harms the robin (ruddock) or the ran (wren), shall ne’er prosper be he boy or man“. Shooting birds on St Stephen’s Day (Boxing Day) was something that happened, but thankfully stopped. I think it’s a tradition that remained stronger in Ireland, although there is also a particular Manx tradition connected with the fair folk. The folklore around both the robin and the wren seem to be more rooted in Christian mythology and lore to be honest.
In Wales, there was a tradition of mock battles between summer and winter at Calan Haf or May Day. Winter would use blackthorn sticks and Summer would use willow and birch sticks, Summer would win and would be crowned May King to accompany the May Queen. Interestingly, the pole was always made of birch. Archetypal battles of sorts may be found in both Welsh and Irish literature; for example, Arawn and Hafgan, but there’s not much to indicate unequivocally a Holly King and an Oak King as Graves would have it. The difficulty with all of this is it is not clear just how old these traditions are, what they were influenced by and how specifically Celtic they may be or, for that matter, what pre-Christian, pre-Roman lore they conserve. That doesn’t invalidate them as traditions by any means, but it’s important to have a clear idea of their cultural influences and context. If we go with the idea that May Day seems to have been the most important festival for the British Celts/Britons, perhaps we should look at Belenos and Belisama.