Anthoceros punctatus remains unrecorded in Glamorgan, but it's usually the easiest species to find in Pembs: poached, rushy corners of cattle pastures are the classic locus, although it also grows occasionally on clayey ditch banks or even on lane banks. Phaeoceros laevis has similar habits but is more regular in arable; the only recent Glamorgan record was Barry's from Staffal Haegr, but there are four 20th century ones as well, albeit not confirmed to species level. Anthoceros agrestis is locally frequent in damp cereal stubbles in central Monmouthshire, along with Phaeoceros carolinianus, and both could be present in clayey arable somewhere in Glamorgan.
All of the hornworts look like mid/dark green thallose liverworts, and could be ignored as Aneura or Pellia if not fertile. Look out for the 'horns' or for male 'pits' in the thallus. Here are a couple of photos to give a search image.
Phaeoceros laevis alongside Riccia glauca in a very mossy stubble field.
Sporulating Anthoceros punctatus on a road verge in Co Cork.
The spores of Anthoceros are black, whereas those of Phaeoceros are orange.
Please go out and hunt for hornworts soon!