If you don't distinguish between regions/countries, that is, the website specifically separates the American version from the British version, and it is only in pure English, the British flag will be used.

That's international practice.

England = England

USA = USA

English = English

American English, there are no exclusive English words, only American English, American English.

However, if the website is divided by countries, including the United States and Britain, then it needs to be distinguished by the American flag and the British flag.