Hi Ludek,
Not so easy to identify this one; by far the best bet is the inscription on the tank, and we can't see it on your lo-res photo. If you want the bike identiied, scan the tank part of the photo at the higest res you have on your scanner (600 or 1200 dpi) and let's have a look at the result.
What I can say is that the period is is early 1920s rather than late. Stirrup brakes on the front rim were mostly gone by 1924-5. There may be some merit in your Barnett theory, but the story goes that Barnett used the brand name Invicta (even after FB were underway in the early 1920s), and from what I can see of the inscription it doesn't look to be the usual Francis Barnett style. FB also tended to use Brampton Biflex forks, rather than the Druids on this bike and the nose of their sloping tank is a little different. In the early 1920s there were literally hundreds of small manufacturers building bikes similar to the one in your photo - as I said the inscription on the tank will provide the best clue.
Cheers
Leon