Why is there no "an" in front of "English Writer" here?

It’s using it as a title/adjective. The subject is actually “George Orwell, who is an English writer”

Look up definite article vs. zero article… basically because George Orwell is a proper noun, it doesn’t require an article (zero article).

The article "an" or "a" is used when speaking of an individual entity but not a specific one. "An Englishman" but not "A George Orwell". Therefore, it's a matter of emphasis. If it was considered important by the writer that 1984 was written by an Englishman, and the name of the author was incidental information then it would be written as a "an English writer, George Orwell". But instead it is considered important by the writer that 1984 was written by George Orwell, and incidental that George Orwell was English.

It's using "English writer" as a set of adjectives to describe George Orwell.

Zero article before the proper noun "Gorge Orwell", and "English writer" is an adjective put before the noun.

They’re called false titles. They don’t require an article (a, an, the). Think of it the same as a title like King.

He’s not an George Orwell

In the phrase "by English writer George Orwell", the kernel of the noun phrase is George Orwell, it doesn’t take an article because it is a name, and "English writer" acts as an adjectival phrase. In the phrase "by the English writer, George Orwell", the kernel of the noun phrase is "writer", it takes an article because there’s only one considered. "George Orwell" is an appositive.

It's being used as an adjective.

If the sentence did not include the proper name "George Orwell", then yes it should have "an", but the presence of a specific name would make "an" incorrect.

Because it's used as a title rather than a job. It gives title with name, same as saying "He is Dr. John Smith." vs. "He is THE doctor"

It’s using ‘English writer’ as an adjective

If you were going to use an article here, it would be “the”, not “an”. “This is a book by the English author George” But “This is a book by an English author”. / “George is an English author”.

Orwell is British or English. If he was some other nationality then to specify that he writes in the English language I would write it as an English (language) writer. Just how I interpret it with no formal training.

"English writer" is Orwell's title and is treated as part of his name here

It's describing a specific person. You would say "an English writer" if the writer weren't named, but they ARE named, so you say, "English writer (\_)"

In that case it would be "the" English writer, because it's about a particular one. And "the" can be dropped in this context because it mentions Orwell by name. "An English writer called George Orwell" would also be correct, but in this example, fame is a factor - it is assumed that you've already heard of Orwell. "an" would be phrasing used if it either wasn't about a specific individual, or if it was about one who you probably wouldn't recognize.

It's being used as a title. "English writer George Orwell" or "Neurosurgeon John Fleming" or "Professor Samuel Duncan." I made those other names up, but they're good examples of how titles generally omit "the."

"English writer" is (in terms of the grammar, at least) being used like a title here. It's the same reason you don't say "a Queen Elizabeth". You *could* use an article here, but it would be "the", not "an". "Nineteen Eighty-Four is a dystopian novel and cautionary tale by the English writer George Orwell."

Using an their while correct, gives off an “you dont know who this is” vibe, but George Orwell is a super famous writer so it gives off an “This was written by The famous English writer, George Orwell

Because it's correct as it is or with the definite article, *the*. Because it names Orwell, *an* sounds very clunky.

cuz its talking about this specific writer

Because it specifies the particular English writer. If it didn't mention George Orwell by name (which would be weird), you would need the article.

We can use adjectives or job titles to refer to people without the article. Usually this is in a context where the person is being introduced, has a title that is relevant to the discussion, and/or is famous for that title. It's like saying "In a statement by Twitter CEO Elon Musk", I assume from this sentence that the statement is relevant to his position as CEO of Twitter. I would not expect the rest of the sentence to be about SpaceX.

English writer is being used as an adjective for George Orwell. It would also be correct to say “…by an English writer, George Orwell” but this case uses no comma, so writer isn’t acting as an object

Shouldn't it be "the" and not "an"? Can someone explain?