Nitra,
Most guns produced in the 1896-1904 proof period were nitro proofed, in fact the absence of the 'Nitro Proof' & 'Maximum' shot load mark is a fairly safe guide to the gun being pre-1896.
Lagopus,
I doubt this gun will have had any 'model' name. It is an absolutely basic Birmingham BLE. I have repaired, sold (and sadly occasionally scrapped) dozens of identical guns with every name imaginable on them.
The harpoon trade mark on the forend iron is that of Charles Osborne who had his factory in Birmingham but a retail premises in Great Scotland Yard in London. He supplied mainly boxlocks to the London retail trade with any name on they wished but this little harpoon trade mark is usually there on the forend iron.
I suspect that this gun was supplied to Churchill fully finished and ready for the sale rack.