Hudson's Bay Company and East India Company could work. But only in the sense of, I could see them being the main authority in the area under the aegis of a more ad hoc British Empire.
They would not be sending ministers to parliament, and they would not have governors appointed, but they would have a lot of soft power at home, and British policy would have a lot of soft power over their policies. They probably would not be making deals with Britain's enemies.
You would need some government interference to keep the Hudson's Bay Company going, though. They had the monopoly. A divergence would be required that made them powerful and competitive enough to maintain a virtual monopoly over the area after the government stops enforcing it. If they were interested in investing in and controlling agricultural and industrial (?) development of the Canadian west, rather than opposed to it, that could help.
And perhaps all it would take for the East India Company to last as long as the Raj would be for the Indian Mutiny to not occur, or to be handled quickly and quietly by the East India Company itself.
They would not be sending ministers to parliament, and they would not have governors appointed, but they would have a lot of soft power at home, and British policy would have a lot of soft power over their policies. They probably would not be making deals with Britain's enemies.
You would need some government interference to keep the Hudson's Bay Company going, though. They had the monopoly. A divergence would be required that made them powerful and competitive enough to maintain a virtual monopoly over the area after the government stops enforcing it. If they were interested in investing in and controlling agricultural and industrial (?) development of the Canadian west, rather than opposed to it, that could help.
And perhaps all it would take for the East India Company to last as long as the Raj would be for the Indian Mutiny to not occur, or to be handled quickly and quietly by the East India Company itself.