To answer your question very clearly, no, there is absolutely no authority in English that is called an academy.
There are however guides, manuals, institutions, authors, dictionaries, and publications that do their best to inform people on usage.
The way they go about it determines what grammar they use. Most do not bother being overly descriptive because it is too expensive and takes up too much room. Hence, they appeal to the indicative mode or say that such is such and such a way. Others that consider some or other usage obligatory are defined as prescriptivists and view English grammar normatively, meaning that according to them some specific variation of English must be used in some particular way and never in any other way. There are many, many such proponents, and they nearly as often conflict with one another. Corpus linguistics (the large bodies of words on the internet that are used to determine contemporary and regional usage via science) will show you clearly that there is no one authority of English and that there are often many alternatives to any one in particular that is taught by a traditional or pedagogical grammarian.
Hence, in contemporary linguistics, the consensus is usually that there is no one correct way to say or write something but that there are standard ways of doing such or conventional ways of doing such. There are still further divisions that are attributed to register (style of context) and region (vernacular or dialect) and therefore in said settings what may be viewed common in one, could be viewed as idiosyncratic in another (in English there are only two conventions, that of Great Britain and that of the US and Canada).