Their motive:

That's funny.

The British of course did need protect their people, but they could also make a good profit off of the fur trade with the natives. If you went to war with someone, lost the war, and then found them asking to trade their erasers,  mechanical pencil and some Gatorade for your five packs of sour patch kids gum, how would you respond. Exactly. So Britain had to get in good with the natives to get the goods.