I've pulled out my Long Tom and found it's a QLD Government rifle, not a Police rifle, as I thought. Seems my memory has lost a little acuity in the past 30 years...
The crows foot missing seems to be pretty evident. User1, Thread No 8, suggests it is may be Queensland Militia, noting the date of manufacture. However, on reflection and a little research, our State Militia forces pretty much changed over to the Commonwealth as of Federation. The AustralianArmy was formed on 01 March 1901, so a 1904 No 1 Mk III would be unlikely to have been a militia issue weapon, as any remaining Militia units would have retained the older stocks, particularly the Martini henrys and the Lee Enfield No 1 Mk 1s. Regular units, as is common, would have priority over the reserve and/or militia.
The clear owner was the Australian Army with the D crowsfoot D mark on the butt.
I've had a much closer look at my Long Tom. I'm grateful for the question Ridolpho, as it's got the grey cells active. I do need to get in contact with the local Military Historical Society and see if they have some advice on rifle provenance.
Below are photos of my BSA No 1 Mk 1* Long Tom receiver ring. The "Q crowsfoot G" is overstamped by the "opposing arrow-S-arrow" 'sold, out of service' mark. Similar to your rifle. The interesting feature is the stylised rack/inventory number applied by the Queensland Government to the receiver and bolt, different to the original sans-serif block stamping font used by BSA during manufacture. Similar to yours, so an evident behaviour of Qld Govt armourers when taking a rifle onto Government ledgers.
Attachment 85245Attachment 85246
I'll see if the Hysterical Society can help out with some specifics on rifle markings and Government ownership. I'm thinking that in the early 1900s the Post Master, Forestry workers, Rangers, Customs officers, Paymasters would be likely candidates for holding a rifle or two in a rack in their offices in little towns scattered across the state. Not just coppers, as not every town with a Government office had a copper posted to the town.
No promises, but I'll see what I can find out and share with everyone.