I'm just gonna be honest, you're being cringe right now. "No it's not my fault I mistook this person's nationality, it's their fault for coming across to me as the wrong nationality" — no, just own up to your mistake, for God's sake, it's not hard. Preferably you wouldn't have made the mistake in the first place — you might've even been able to avoid it if you'd just read more carefully, given it even a second longer of thought, and weren't so quick to make assumptions.
Take time out of your day and think about why you come across br*tish
I'm just gonna be honest, you're being cringe right now. "No it's not my fault I mistook this person's nationality, it's their fault for coming across to me as the wrong nationality" — no, just own up to your mistake, for God's sake, it's not hard. Preferably you wouldn't have made the mistake in the first place — you might've even been able to avoid it if you'd just read more carefully, given it even a second longer of thought, and weren't so quick to make assumptions.
You have laid bare how your mind works: "If someone's not from the USA they're from the UK"
Learn a bit about the world before talking about it.