Why do we say "spoken English" rather than "speaking English", while "English-speaking world" rather "spoken-English world"?
Since "English in writing" is right, how about "writing English"?
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Whilst written is indeed a valid option as the participle of write, it is not being used as a participle in "written English", it is not literally referring to a written piece of text. Rather, the word written in this context is the adjective describing the noun as "expressed in writing (distinguished from spoken ).", not the actual act (verb form) of writing.
These are different grammatical and syntactical situations; it's not like "spoken English" is right while "speaking English" is wrong, like your question seems to suggest. They mean different things.
In "speaking English" the "main" word is "speaking", which is a gerund (a verb that has been turned into something that functions like a noun).
In a sentence that would look like that...
Speaking English is a skill that is different from reading English.
..."Speaking English" is the subject of the sentence. This sentence also has another gerund—"reading". One thing is different from the other, and these things are processes of either speaking or writing English.
Another example of "speaking" as gerund:
Speaking several languages will increase your chances of finding a good job.
Here again, there is a second gerund—"finding". X will increase your chances of what? (a question that can be asked about nouns)—of finding a good job.
On the other hand, in "spoken English" or "written English", the "main" word is "English"—as a language. It means the language itself, as it is spoken or written—the whole collection.
So, speaking English or writing English is what you do (or what any other person does). Spoken English is how the language is when it is spoken. For example,
Rules of syntax are not followed as stringently in spoken English as they are in written English.