"Dear Professor" vs "Dear Mr": differences between British and American usage

In British English, is it acceptable to address a professor as "Dear Professor X" when writing a formal or informal letter? Does it sound natural?

Why I am asking this question:

I was looking through the list of differences between the British and American editions of the first Harry Potter book by J.K.Rowling.

In the first chapter of both editions, a character named Hagrid keeps addressing Professor Dumbledore as

Professor Dumbledore, sir.

However, when Hagrid writes a letter to Dumbledore, the two editions use different forms of addressing:

U.K. edition:

Dear Mr Dumbledore

U.S. edition:

Dear Professor Dumbledore

Edit: Everywhere else in the U.K. edition, he is still "Professor Dumbledore". This letter seems to be the only exception. If he normally calls him "Professor", why he would write "Mr" in the letter?

Why "Mr" instead of "Professor"? Is "Dear Professor X" inappropriate in the U.K. for some reason? Or it just doesn't sound natural?

Answer

I think OP has the issue of "appropriateness" the wrong way round.

It's quite common in Britain not to address doctors and professors by that title. They're just plain "Mister", the same as the rest of us. I can't say exactly why - maybe we're a bit more egalitarian.

Clearly the change was made specifically for the US market, where I guess this usage is considered somehow "impolite" (disrespectful to either the office or the holder of the title).

I must admit I find it odd that such a change should be made to an English-language book in this way. But obviously the UK wording came first, so arguably the onus is on Americans to explain why they worry about such niceties (or why their book publishers think they might worry).