What if the American West had been settled by the British instead of the Americans?

This question I think has interesting and far-reaching consequences. Would the Mexican-American War still have occurred, or would Mexico have perhaps become a British dominion? Alternatively, would this make another Trek War-esque event an inevitability, as the British slowly confiscated land from the Mexicans and other native peoples? Would the US proper still have expanded all the way to the Pacific? <br><br>Within the US, would this have led to a unified American identity? Or would this have instead created a situation in which the segment of the US that had been settled by the British would have seen itself as culturally distinct from the rest of the country?