In many species of birds, the belly feathers are very dark at the base, with the normal color only occupying the tips of the feathers. So any unusual wear, or simply messiness, of the feathers, will show black in that spot.
If your bird has been scratching at a tick, or has been brooding eggs or chicks (uh, where are you located? I've been in the southern hemisphere a lot lately...) or simply has been roosting someplace uncomfortable, you may see a black "lining" that's normally hidden below the normal color.
Where are you located? (edit 2: Hampshire - I assume that means the one in England. I'm not having a good day for reading comprehension...)
What species of wren? (If you don't know, we can guess based on your location.) (edit 2 1/2: and I think in England there's only one "wren" to choose from...)
Edit:
I didn't read your post #4 very carefully, did I? If it's been unchanged for weeks, it's not likely to be a temporary ruffling of the feathers. I suppose heavy wear is still possible, but that would call for some kind of explanation that I can't think of. So I agree "abnormal plumage" (likely genetic in origin) is the most likely.