Pattern welded rough forged tubes were certainly sourced from Belgium

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Not so fluid steel.
Deakin and Johnson patent "Punched Steel" (presumably Bessemer) was used briefly in the mid-1860s.
Wm. Powell & Son used Whitworth steel for barrels in 1875.
P. Webley & Son began using Siemens steel barrels about 1880.
The first Purdey Pair Nos. 10614 & 10615 were delivered January 1, 1880 with the “New Whitworth Fluid Pressed Steel”.
William Evans stated he preferred Siemens barrels in his 1893 catalog.