"The British never used inferior steels in their weapons"
It's not a question of inferior steel, and I never claimed it to be such.
It's a question of design, construction, and what's happened to that gun since it was made better than a Century ago.
The cylinders on the BP-era Webleys are not as robust (steel thicknesses) as the later Cordite Webleys.
The heat treating on early Webleys is pretty much non-existent. I've been told, but have no way of confirming it, that the British didn't start heat treating Webley frames or cylinders to any consistent specification until the adoption of Cordite.
Smokeless powders have very different burning characteristics than black powder and even if overall pressure is below black powder levels can still stress an old gun in ways that were never expected in BP days. That's why you see warnings not to shoot smokeless loads of any kind out of BP era pocket revolvers. They can eat BP loads all day long, but even light smokeless loads can have an adverse effect on the gun's health.
That's why the British withdrew from service all BP era Webleys when the switch was made to Cordite. Even though overall operating pressures were the same, Cordite still put stresses on the guns that they simply couldn't handle.
As WA notes, given that this gun was converted (perverted?) it's very possible that it has been fired with .45 ACP ammo and that there are larger issues just waiting to happen because of that.
The final reason why I wouldn't shoot that gun with even light smokeless loads? It's too nice looking to even take the chance. BP and even Pyrodex are readily available and will serve the purpose just fine.