According to the late Clive Law's excellent research, most of the approximately 1,588 No. 4 Mk. I* (T) Canadian Long Branch made sniper rifles were sent to the Britishmilitary. Unlike other small arms, WWII Canadian snipers in Europe received their rifles from the British "pool" so a Canadian sniper could have any of the versions in North West Europe. (Reference: WITHOUT WARNING by Clive Law)
"Stencollector" in Manitoba has a BSA No. 4 Mk. I (T) with a Canadian C/|\ (arrow inside the C) and this is the only one that I am aware of. One BSA was found with a Canadian marked M1907 sling on it but there were no other indications of Canadian ownership seen. I was able to work a deal for that sling and I now have that sling on a Long Branch No. 4 Mk. I* (T).
A number of Canadian military museums, such as the one I am Curator of, have British No. 4 Mk. I (T) rifles in their collections, but most were likely donated by people who had bought them surplus. I know this is the case for the mismatched one in our 12 Service Battalion Museum. Sadly, wartime photos do not show the serial numbers :-( but both Mk. I and Mk. II cocking pieces can be seen.
The Princess Patricia's Canadian Light Infantry (PPCLI) Museum in Calgary has a British No. 4 Mk. I (T) but I do not know what, if any, provenance for it. It is rifle AQ2892 with matching No. 32 Mk. I HBM Co scope # 4376 The Mk.I modified backsight had been removed. I have an autobiography of a PPCLI sniper section commander who wrote that the Commanding Officer ordered him to take a sniper rifle which has been used by the battalion in WWII, out of the museum and to take it to Korea with him and put it to good use. I have not been able to find out if this AQ2892 / 4376 is indeed that same rifle. WE cannot assume that it is unless the records are good, and old military museum records are notorious for their lack of detail, if they even exist.
Back in Canadain late WWII, in peacetime and then in the Korean War, Canadian made sniper rifles were issued to Canadian troops.
I agree with Roger Payneabout the bracket in the Dutch museum being numbered to a 1943 BSA made No. 4 Mk. I (T). I too am puzzled by the three rather than four numbers following the letters as every other case I have recorded has 4 numbers e.g. AV0173, AV0189, AV0192, AV0210, AV2240, AV2281, AV2287, and AV2293.