According to Boothroyd, Beesley moved to 2 St James St in 1900. Can't comment on the exact SN, but that certainly fits with the proofmarks, which are without question (because of the MAXIMUM mark) 1896-1904.
Slate, something else to check would be bore diameter/wall thickness. That gun does not show any indication of reproof, which means the bores would have been .729 (or very close) from the maker. If they're .010 greater, that would make them out of proof--although on a British gun that old, one would almost expect some honing/polishing to have taken place. But if they're significantly larger than .729, that might also mean wall thickness is questionable.
