Britain's naval response in a hypothetical war with the United States

If the United States invaded Canada, did Britain plan to abandon the theater and fall back on India?

No. The plan relied on the Royal Navy's global position to obstruct the Panama route, threaten the eastern seaboard, and contest American fleets along their alternative approaches.

Britain did not plan simply to abandon Canada and concentrate elsewhere. The naval concept was to block the Panama Canal, strike the eastern seaboard, and force American ships to take long routes into prepared British fleet areas. Home Fleet would face the U.S. Atlantic Fleet while South Atlantic, Mediterranean, China, East Indies, Australian, and New Zealand forces covered alternative approaches. Imperial geography shaped contingency planning even for an improbable Anglo-American war.