Welcome to the community! We haven't been so active lately, but I'm sure you'll find support here.
Did your adoption take place in the UK? If so, it is a relatively simple procedure.
I did it about 10 months ago. I went to this website:http://www.gro.gov.uk/gro/content/adoptions/
where I sent off for my original birth certificate, then my adoption certificate. This took about a month, and when I had all the details of my birth parents' names, I put my name down on the Adoptions Contact Register:http://www.gro.gov.uk/gro/content/adoptions/adoptioncontactregister/
Within a couple of weeks, I had the name and address of my birth mother. We exchanged letters and eventually met up!
Even though your birth mother moved back to Canada, her details will still be on your birth and adoption documents, and there will be plenty of Canadian contact and search registers you can try when you get to that stage.
Good luck with it, and let me know if you need help or advice from someone who has done it.