Peter, in a 2011 Update of the British Isles Diptera Checklist (edited by Peter Chandler) there are only two entries for the genus DESMOMETOPA in Britain:
DESMOMETOPA Loew, 1866
palpalia (Wahlberg in Zetterstedt, 1848 - Agromyza) New to List, Note 1
(? discipalpis Papp, 1993)
sordida (Fallén, 1820 - Madiza)
(m-atrum (Meigen, 1830 - Agromyza)
What exactly have iSpot and David Noton, of the Natural History Museum, said about your flies? I suggest you refer an actual specimen/s to our County Recorder for Diptera, Del Smith. A brief look on the internet suggests Desmometopa m-nigra is a species recorded in southern Europe and some other warmer parts of the world and its presence in Britain should certainly need confirmation of microscopical examination of an actual specimen/s. It is likely that all the species in the genus are pretty much identical in overall outward appearance.