Mike: several guys are out there trying hard to identify generic damascus patterns (3 iron crolle) and specific named patterns (Oxford, Boston, Horse-shoe, etc.) Part of the problem is that there are so many variants of each crolle pattern. These segments are all Belgian, 2 iron crolle, 'browned' rather than 'black and white', and all with a different pattern

Some patterns can be identified as specifically Belgian (ie. I've not seen them on a British gun): Chain, Etoile (Star), Stars & Stripes or American Flag Bunting, Chine', Bernard, Leclerc, Pieper P (Remington.) It's probably safe to say that any 5- or 6- iron crolle is Belgian.
Other patterns are found on both Belgian and British brls: Horse-shoe, Boston (large scroll 2 iron crolle), Oxford (smaller scroll 3 iron crolle.
British Laminated Steel has several variants, but does indeed seem to be uniquely British.
The 'English Damascus' album has both 'browned' and 'black and white' patterns, and a couple that I have yet to identify (name) that could be uniquely British
http://www.picturetrail.com/gallery/view?p=999&gid=18059733 Bottom line-the vast vast majority of brls used by US makers were of Belgian origin, and until we can confirm a uniquely British pattern, there may be no way to confirm the source of the barrels (which almost never have maker's marks.)