Despite being considered non-standard, it appears that the usage of ***either…or*** and ***neither…nor*** can extend to more than two items with the Bard himself and Dr. Samuel Johnson ([The Oxford Dictionary of National Biography calls him "arguably the most distinguished man of letters in English history"][1]) using the terms with more than two items. So this usage likely started on the British side of the pond as OP mentioned.

According to [grammarphobia][2]
> Either” and “neither” usually refer to only two things, but not always.

>When “either” showed up in Old English as ǽghwæðer (also contracted as ǽgðer), it meant “each of two.” And when “neither” showed up in Old English as nauðer (næþer in early Middle English), it meant “none of two.”

>Yes, there’s clearly an etymological two-ness about the terms. And as we’ve said, that’s the way “either” and “neither” are generally used.

>However, writers haven’t been confined by etymology when the terms are used to introduce a series, as in these examples from Shakespeare:

>“They say there is divinity in odd numbers, either in nativity, chance, or death” (from The Merry Wives of Windsor, circa 1597).

>“You know neither me, yourselves nor any thing” (from Coriolanus, c. 1605-08).

>If Shakespeare’s not good enough for you, how about Samuel Johnson? His biographer, James Boswell, quotes the great lexicographer as saying “neither tea, nor coffee, nor lemonade, nor anything whatever.”

>The Cambridge Grammar of the English Language notes that the duality of “either” and “neither” is weakened when they’re used as conjunctions to introduce a series.

>The authors, Rodney Huddleston and Geoffrey K. Pullum, say the two terms can be used “in multiple as well as the more common binary coordination.”

>Huddleston and Pullum give these examples: “either Kim, Pat, or Alex” and “neither kind, handsome, nor rich.”

>Standard dictionaries generally accept the use of “either” or “neither” to introduce a series of more than two items.

>Merriam-Webster Unabridged, for example, says “either” can be used “before two or more coordinate words, phrases, or clauses joined usually by or.” It defines “neither” as “not one of two or more.”

>However, dictionaries say “either” and “neither” refer to only two alternatives when used as an adjective (“I’ll take either flavor, vanilla or chocolate”) or a pronoun (“Neither [of them] for me”).

>We gave examples above of Shakespeare’s use of “either” and “neither” with more than two items. We’ll end with an example from Hamlet (c. 1600), in which he overdoes the usage to emphasize the pedantry of Polonius:

>“The best actors in the world, either for tragedy, comedy, history, pastoral, pastoral-comical, historical-pastoral, tragical-historical, tragical-comical-historical-pastoral, scene individable, or poem unlimited.”


  [1]: https://en.m.wikipedia.org/wiki/Samuel_Johnson
  [2]: https://www.grammarphobia.com/blog/2017/08/either-neither.html