As long as you don't set foot on British soil you'll be fine. But that's less simple than it sounds. Don't book a flight that connects in the UK, sure. But what if your NYC-to-Munich flight has engine trouble and needs to make an emergency landing in London? You are screwed: You'll be pulled off the plane and taken to jail.
Will the US embassy get involved? Of course. Will they get you released? Maybe, but it's not guaranteed. And you are in for a bad time regardless.
Will the US embassy get involved? Of course. Will they get you released? Maybe, but it's not guaranteed. And you are in for a bad time regardless.