How call English language which people use in England? There is American English, Australian English, New Zealand English etc.
But the word "British English" means English from whole Great Britain (England, Scotland, Wales and Northern Ireland) "English English" sounds a bit strange

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I agree. English English does sound strange, and that's probably why it's not called that.
Since all British schools in the United Kingdom teach the same form of English (allowing for accents in different counties and countries), it's just referred to as British English.
Scottish English is the same as English English.

You'll find that a lot of British people will simply refer to it as "Proper English".... :-D