Dear TaVaris,
@Kennewick Man
Yes, it's part of the fun identifying these mysteries. Luckily you had the enigmatic 'Birmingham', and after that it was the chainwheel...
There's quite a bit more information here (in english), and the bike seems to have the same fork as yours.
1904 Light Roadster Bicycle built from ‘B’ pattern BSA fittings
onlinebicyclemuseum.co.uk
The owner of the site is a member here.
@Wing Your Heel
Have fun with your search.
Best Regards,
Adrian