My guess: The same yet unidentified Birmingham shop that actually made the Mannlichers and Mannlicher – Schoenauers for W.J.Jeffery and others. Jeffery was a dealer or retailer who did not make "his" guns himself. Instead, they had them made to their specifications by the international guntrade in Britain,Belgium and Germany. Recently I have seen a .404 Mauser with a somewhat "Germanic" stock style with oval reinforcements and wedge in foreend. On the outside: London proofmarks and W.J.Jeffery address on barrel. Under the barrel: German, Suhl proofmarks and a "A.Schüler, Suhl" stamp. So it was made for Jeffery by Schüler.
Contrary to common belief The Steyr factory started to offer their own sporters in 1905 only. They never sold actions only or barreled actions. But all the time since 1892 they sold complete military Mannlichers from their export models production to all comers. British gunmakers bought those complete military rifles and "sporterized " and refinished them to various degrees to their tastes. "Economy" grades merely had the military stocks cut down, checkered and slimmed and the sights replaced, while upgrade ones like this one were completely restocked and had all the bells and whistles like peep sights and trap grip caps added. Many such Mannlicher and Mannlicher – Schoenauers were reworked by G.Gibbs, Bristol, others by unknown Birmingham shop(s). The Gibbs sporters are easily recognisable by their distinctive stock style and a B – prefix serial number. I have seen such Gibbs sporters signed and retailed by other name gunmakers like Rigby, Purdey and Atkin. Other British gunmakers like Jeffery had their rifles made by the Birmingham guntrade. After WW1 there were no more miltary Mannlicher –Schoenauers in Steyr production or widely availble. So the British guntrade had to buy in complete sporting rifles from Steyr and complete restocking was not necessary any more.