Pamela â€” there should not have been any difficulty with your bowl, as it is both described and pictured in Bowey, Parsons & Parsons, 2004; fully described in Dodsworth, 1987; and is in my set of photocopies of Bagley illustrated advertisements from The Pottery Gazette and Glass Trades Review
My response was delayed because I cannot access large images pre-formatted in a web page from home, I can only access large images directly in .jpg format, which allows my browser to re-size them. Hence I had a quick look at your web page yesterday at college, when I needed a break from learning MS Access.
I noticed then that your flower block is marked "BRITISH MAKE". That's OK for Bagley, who, from time to time, used all three of "BRITISH MAKE", "BRITISH MADE" and "MADE IN ENGLAND", with "BRITISH GLASS" reserved for clocks, as the clock mechanisms were not British. Is your bowl marked? It would be most unusual if it was marked on the inside, as the same mould was used for a lampshade (danger of relief lettering causing hot spots, cracking the glass). If it is marked it must be on the rim or the outside, although I suspect it is not marked, as Dodsworth would have noted it.
The above was written before seeing the three previous replies.
As for the similarity of the Davidson No. 8 Semi-dome, the Bagley 227 flower block, and the Jobling Flower block, I can't tell the difference with unmarked examples, and I have had many hundreds through my hands. All it indicates to me is that these complex moulds, with the unusual process involved, were all made by the same mouldmaker, probably either Davidson's mouldmaker or a freelance.
I do not believe the block in your 3003 bowl, Pamela, is a later addition. That size is quite scarce, and would be difficult to match on colour.
I hope that helps.