Polydesmus coriaceus
Polydesmus species are easy to recognise to genus but require examination of the male gonopods or female epigyne to identify to species. The gonopods are quite 3-dimensional making it difficult to show the whole structure in photos taken through a compound microscope.
This individual, found in a pitfall trap, was readily identified as Polydesmus gallicus using the gonopod drawings in Gordon Blower's 1985 book on Millipedes. A bit of googling led to the conclusion that gallicus is now known as coriaceus but then I came across a paper about Iberian Polydesmus which included a diagram of gonopods which cast some doubt over my ID, with inconstans looking much closer than it had seemed in Blower's illustration.
The outer, longer arm of the gonopod shows a swollen base, abruptly narrowing before it joins whatever the bit of anatomy the gonopod joins to is called (or is it still part of the gonopod?). Blower only shows this shape for 'gallicus' but the Spanish paper shows inconstans having a similarly swollen base (albeit perhaps not narrowing in the same way at the very base). The Spanish paper also shows a similarly obvious triangular projection below the tip of the outer longer arm for inconstans, whereas Blower had shown this as being smaller than on my specimen. Moreover the Spanish paper showed a difference in the tip of the shorter inner arm of the gonopod between the species, this being more curved (like my specimen) on inconstans.
All this made me wonder if mine could in fact be inconstans but in the end I stuck with my original ID. The bit of the projection below the tip of the longer outer arm of the gonopod that sticks out proud from the inner side of the arm is triangular in shape on all illustrations, but the precise shape of the projection seems to differ. On my individual the triangular projection is only joined to the arm it projects from for just over half the length of its base, so there is a further edge extending up from the bottom of the triangle to the start of where it is joined to the arm (this shows best on the last of the photos below). This appears to be matched by both illustrations of coriaceus but on both illustrations of inconstans it looks as though the bottom edge of the projection merges smoothly into the inner edge of the arm. Also both sources show the inner arm of inconstans as being shorter, only reaching the triangular projection, whereas on coriaceus (and mine) it clearly passes the triangular projection and almost reaches level with where the tip of the outer arm starts to turn inwards.
male Polydesmus coriaceus showing gonopods, North Elmham (Norfolk, UK), 24th March 2022