I will put this out for the benefit of anyone seeking "the" way to do anything in written English:
There is no single authority on English punctuation. In fact, one could argue there are tens of thousands of different authorities— style manuals— as each publication may have particular rules it insists upon for certain scenarios. That is why discussions of it are so contentious; people taught one way in school about the right use of the Oxford comma, sentence spacing, or apostrophes in pluralization cannot bear that people in other schools were taught that the exact opposite was correct, and that there is in fact no "official" way that is universally applicable.
That is not to say that there are tens of thousands of conventions. The basic usage of the semicolon, like all common English punctuation except for quotation marks, does not change by locale. The introduction to it from Fowler's Modern English Usage is substantially similar to those of other common references:
[The semicolon's] main role is to mark a grammatical separation that is stronger in effect than a comma but less strong than a full stop [period]. Normally the two parts of a sentence divided by a semicolon balance or complement each other as distinct from leading from one to the other (in which case a colon is usually more suitable)….
It is also used as a stronger division in a sentence that already contains commas….
Another popular standard in the UK is the Oxford Style Manual and New Hart's Rules, published under various names, and not to be confused with the University of Oxford style guide or the Oxford University Press house style, which precede it in my search results. In the U.S., I would wager the best-known reference for non-journalistic, non-scholarly writing is the Chicago Manual of Style, whereas the major journalistic organizations follow the AP Stylebook or a derivative thereof. Whether these are appropriate for your research or not depends upon the contents of your corpus.
Where the style manuals vary is on the finer details of punctuation— whether or not it may be used with coordinating conjunctions, how many spaces should be placed around it, whether it should be printed inside or outside quotation marks, how to integrate it where parentheses or dashes are used for internal punctuation in a list.
Note that this lack of central authority applies to all English, spoken and written; there is no equivalent to the Académie française. The Meta.EL&U thread What good reference works on English are available? provides a reasonably good sampling of commonly used standard references.