Have you ever heard of Monaco? Liechtenstein? Luxembourg? Malta? The idea that areas of a few hundred thousand people are too small to be independent is ridiculous. You mention loyalty, why should I feel loyalty to the British state? I did not choose to live here.
Cornwall is a recognised political entity within the United Kingdom, another political entity. Both political entities have democratically elected governments. If Cornwall were to vote for independence from the UK, the UK government would have no choice but to accept it. Were it to refuse that, it would face huge national and international pressure to respect the democratic process. The UK's reputation as a democratic stronghold would be tarnished were it to refuse Cornwall's independence. Any military action would only cause outrage in the liberal world. The ability to choose how you are governed is one of the fundamental ideas behind democracy. You cannot pick and choose which parts of democracy you follow. If you do, then you're not a democracy.