Perhaps because we read books by English authors, many Americans mistakenly believe (consciously or subconsciously) that British English is more correct than American English. (Our cousins across the pond will no doubt insist that it is.)
But if you are an American writing in America, and not a Brit writing in Britain, British English isn’t more correct than American English. It’s incorrect. Every American style guide will replace your “travelling” and “colour” with “traveling” and “color.” It isn’t “grey,” “humour,” and “football.” It’s “gray,” “humor,” and “soccer.”
The one which trips me up most often is “grey,” which looks as correct to me as “gray” does. I can readily see the difference between “travelling” and “traveling,” although I had trouble with these at age 14. But for some reason, I (like many Americans) often can’t remember which gray is which.
The word “soccer” will strike certain Americans and all Europeans as silly. You kick it with your foot. But we already have a sport called football, and thus every style guide in America will insist that you use “football” to refer to the sport played by Tom Brady, and “soccer” to refer to the sport played by David Beckham. What is anachronistic (that football describes a sport in which passes are thrown and touchdowns run) is not incorrect.
Naturally, a Brit writing about Americans will not use the word “soccer” or “honor” or “truck,” but will instead refer to “football,” “American football,” “honour,” and “lorry.” Here in America, a truck is a truck, not a lorry, and your book will not go to print without a copyeditor correcting “lorry” to “truck” and “football” to “soccer.”