Cockerill-Sambre can probably be blamed for the demise of pattern welded tubes much more than Sir Joseph.
I still don't know the source of 'Armory Steel' which appeared on the Crescent Fire Arms Co. Model 6 hammerless double in 1904, and on the Meriden Fire Arms Co. A.J. Aubrey double in 1905, at a lower cost than Twist or Damascus, but by then the transition from Pattern Welded barrels was in full force.
The Parliamentary Papers, Volume 122, Great Britain Parliament House of Commons reported in 1905 that 1,500,000 rough forged or finished fluid steel barrels were being produced annually by Belgian factories, a large proportion of which was for the U.S. market.