In the British Isles there are 12 species of Coniopterygidae. Unfortunately, these species cannot be identified from photographs or in the field, to identify the species you need to collect specimens and clear their abdomens to be able to view the genitalia. It is only males that can be easily identified.
To start to identify your coniopterygid, first look at the hind wings. Are they greatly reduced (see image below), if they are click here, if they are not greatly reduced click here.
Next, look at the shape of the reduced hind wings (see image below), are they subrectangular, long, and strap-like, if yes you have the genus Conwentzia (click here). If they are subtriangular and short, you have Helicoconis (click here).
If your hind wings are not greatly reduced you need to look at the crossveins between R and M (RMCV) (see image below), are there two (click here) or one (click here) crossveins present.
If you have two RMCV crossveins have a close look at vein Cu in the forewing (see image below). If Cu is sinuous, you have the genus Aleuropteryx (click here) if it is straight, you have Helicoconis (click here).
If you only have one RMCV, you need to look at vein M in the hind wing (see below image). If M is simple, you have Coniopteryx (click here), if forked click here.
For insects that have a forked M in the hind wing, you need to look at the relationship of the crossvein MCCV and the fork of M (see below). If MCCV is basal to the fork of M then you have Parasemidalis (click here), if MCCV is after the fork of M, then you have Semidalis (click here).