I don't know of one specifically for sporting arms. They were huge and had several facilities that could produce something for every need. I think that they also imported steel and melted it down, adding elements to make their own brew. I would guess the steel came from the River Don Works, Sheffield but that's just a guess. They also had a Birmingham facility and I could dig up the other locations if need be(Barrow, Birmingham, Erith(other machine guns), North Kent(Crayford???(Maxium guns), Sheffield). The only mark I can find is on the tubes just forward of the flats. A better image capture may not be possible and the tube forger's mark may be that of Vickers or note the 1st pass thru the Birmingham proofhouse???:

Pfeil & co. may have been an steel agent or peddled Vicker's wares.
Kind Regards,
Raimey
rse