Those chinstraps are US issue and we didn't have them until we bought the US M1helmet in the end '50s... Also you can clearly see it's marked with the US ordnance flaming bombs. If you look inside a US issue M1917 Kelly helmet I think you'll find these. They would have made replacements until they were out of service and that took until into WW2.
Here's a site that sells repros to show you what I'm talking about. Military Reproductions
You need the liner for a Brodie I think. Here's what you need, see Collector's Source in Acton On. Canadian MK II helmet C.L./C. 1942 - Headwear - Collector's Source, Military Collectibles Online