Re: H&R 32 break top
You have a 2nd Model PREMIER SMALL FRAME 3rd Variation made between 1909 and 1913. It is chambered for the .32 S&W (the shorter one) smokeless cartridges. Blued finish in that mod and var. is scarce adding to collectibility. Barrel length (anything other than the standard 3") will add more value. This gun would top out around $290 US in the current market - lesser condition, lesser value down to under 100 bucks for parts gun.
The proof marks are for the Birmingham England proof and view house. My guess it was sent to England (sold into England) by H&R at the time of manufacture - H&R sold lots of guns to England, the Colonial Holdings and later Dominion states and at one time was licensed to "proof" guns meant for such sale at their factory in Worchester, Mass - for sale without further proof at destination. I'm not clear on whether H&R applied the markings, or if your gun was final proofed in Birmingham. In any case, you have a fine collectible item - can't tell you how it got to Canada, though.
A little more info on the physical attributes of your gun, or a couple good pics would satisfy my craving to see H&Rs from other parts of the world as well as allow better eval. of the condition and potential value.
Jim Hauff ~ H&R Collector In Memory of Bill Goforth and Jim Ritchie