A number of things here. First off, the British (actually the English) began exerting control over parts of what is now Canada from the 17th century. In particular the Hudson's Bay Company claimed authority over all the lands draining into Hudson and James Bays, which is a large part of modern Canada. Then in the 18th century Britain ousted the French from what is now eastern Canada
The English takeover of Canada began in the 17th century with the establishment of French settlements and culminated with the British victory in the French and Indian War (1754-1763). The Treaty of Paris in 1763 transferred control of Canada from France to Britain. Over time, Canada gained autonomy, ultimately becoming an independent nation while remaining part of the British Commonwealth.
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