Learn English – “have” vs.”have got” in American and British English

I have looked through several questions and answers on EL&U, and often there is an indication that American English prefers "have" while British English prefers "have got". In addition, there are several references to "have got" being more informal than "have" (e.g.: When to use "have" and "have got", “Do you have” vs “Have you got”). But where is it considered more informal? In American English alone or both American and British English?

This point may seem obvious to those who made the above mentioned references, but the fact is that even the most fluent users of English in my country will say without a doubt that 'have got' is the preferred usage in the UK and, therefore, it must also be more formal. Why? Because in an academic environment, the more informal structures are generally frowned upon, outside some specific spoken exercises. And if the teachers insist on using "have got", it follows it isn't informal.

So, is the teaching of (British) English in our schools transmitting the wrong idea?

EDIT: I'm adding some information in answer to the comments.

I'm mainly concerned with the idea of possession:

I have got a cat vs. I have a cat and She has got a dog vs. She has a dog

As mentioned in the comments, every (Portuguese) student will be told that "have" and "have got", when it comes to the idea of possession, are absolute synonyms, the only two differences being:

• 1. "have got" is preferred by British English, "have" is preferred by American English
• 2. the negative and interrogative structures differ

I have never heard of any distinction in formality. In fact, I was rather surprised when I went through the EL&U archives and read about it.

So, would "I have got a cat" be as formal/informal as "I have a cat"?

And how do British and American English look at its formality/informality? Is it the same?