Found this carrier picture in a Old Book.

[Ron Pier]

On the nearest bike which is a BSA WM20 you can make out the little brass contract plate on the rear mudguard. Just above that and in the shadow of the rear carrier is a rear lamp (Known as a "Fag End") It's on two little legs in the middle of guard. I don't think the other bike is a BSA. The bottom edge of the rear guard looks more like Norton or Matchless. But the more I blow up the picture the fuzzier it gets. Ron