Did Britain only believe her land rights stopped at the boundaries of Indian habitation? Or did Britain believe that land from East coast to West coast, with exception to French or Spanish territories, was rightfully hers?
Edit: spelling
The British claimed authority over the Ohio country, for which the American colonists had fought the French and Indian War, and undeniably was a cause of that conflict.
The actual extent of that authority, and whether it really existed, is a bit vague. With the Proclamation Line along the Allegheny Mountains, the Crown attempted to prevent incursions into this territory by the American colonists, but they never refuted their claim to rule of it. Nor did they seek to revoke any rights of the native nations therein.
What we can say with certainty is that the British claimed the thirteen American colonies, Quebec, Nova Scotia, and Florida. They did exert real authority over all of these colonies, even if for only a brief time. Florida returned to Spanish control after the Revolutionary War.