I think it is unlikely that the barrel is a replacement, it's hardly likely that anyone would go to the trouble of having a roll die made to replicate the original 'factory' markings.
It's more likely perhaps that a round barrel was standard, as they are size for size cheaper to produce than octagonal or half and half designs. The small bore target rifle market in Britain in the early 1900's was a very competative business and anything that reduced the cost of producing the rifle without effecting its accuracy would be siezed upon by the manufacturer.
I think we have all seen firearms advertised in advance of production that differed somewhat from the original description when it was marketed. Its happened to me.
The .22 Long Rifle cartridge was well established by the time this rifle was advertised, the advert stated that it was being chambered for a specific .22" LR round by a named manufacturer. The .22" Long Rifle cartridge was developed by Stevens in 1887 by taking the case from the .22" Long cartridge and fitting the 40 grain bullet from the .22 Extra long cartridge.
Small Bore rifle shooting was really at it's zenith around the end of the first decade of the 20th.C. in Britain and there was a lucrative market for rifle sales. Stevens can't be blamed for wanting to cash in on such a market. Stevens problem was 'how to do it'
The most economical way would be to have the rifle made in Britain in it's entirety. Get a manufacturer to build the rifles on an existing action, or surplus actions from a production over-run using sights and sight insert holders that were already in mass production and therefore cheaper than any new design.
The clue's are tantalising, almost certainly a Birmingham Gunmaker, but who? BSA, probably, but Webley or Greener are possibilities. Matching the action to one known to be made or imported by one of the Birmingham Gun Makers would be a good starting point.
Harry