Official English language rule book?

No single institution governs English use. Nor is there a definitive 'rule' book that covers all contexts. 

The structure of the English language dictates some of its grammatical conventions. Adjectives generally precede nouns, for example: the 'red car' rather than the 'car red'.

Within these confines, however, English has evolved organically, through custom and practice. As David Chrystal has pointed out, it is a 'democratic language', responding to usage rather than rules imposed from above.

Style Guide

Of course, there are conventions about correct usage.  The closest to a universal standard guide is Fowler's Modern English Usage, first published in 1926. This remains popular, but its judgements should not be regarded as definitive.

Other publications, academic institutions and companies have what are known as style guides. The Times Style Guide (2022), for example, offers:

A practical guide to English usage with preferences ... including capitalization, hyphenation and variant spelling... it also advises on terms that should be treated with caution and defines words that are easily confused.

 

The Oxford English Dictionary

One of the most important guides to what is considered 'correct' is  The Oxford English Dictionary. The OED monitors multiple sources to determine whether a word is in general use in British English. It often serves as the arbiter on contentious questions, such as which words can be used in Scrabble.

Grammar and the Use of English

Other key reference works apply general rules adapted to specific contexts. Thomson & Martinet's A Practical English Grammar is widely used by students of English as a foreign language.