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Why did I think this? Because I have been consigned literally millions of movie posters from every corner of the globe, and I noticed that whenever I would be consigned movie posters from England they would almost NEVER include English one-sheets, but instead included British Quads, and that when I DID get consigned English one-sheets, they almost always came from the above four countries (Canada, Australia, South Africa, and the U.S.), and that I almost NEVER received British Quads from any of those four countries. In addition, I have not encountered English collectors who can tell me they saw English one-sheets on display at their English cinemas.
And that made perfect sense! All of those four countries had their own one-sheets, so theaters could easily display English one-sheets in the same display cases or frames, but none had a size like a British Quad, so they couldn't display those. And in addition, the U.S. had three-sheets, six-sheets and 24 sheets, so it made sense to make those for English movies to export to the U.S. (although oddly, they called them by double the U.S. names, six-sheets, 12-sheets, and 48-sheets, and they made them slightly larger, likely having to do with the English printing presses at that time).
But I never had absolute proof of this, until I was consigned a 1949 English pressbook for Hamlet, which contains the "smoking gun" proving this, in the form of two pages reproduced below! It confirms what I wrote above. It has two pages in the back, and one is labeled "POSTERS FOR UNITED KINGDOM AND EIRE", and that page shows the British quad, the door panel, and the English half-sheet. The facing page is labeled "POSTERS FOR OVERSEAS", and it shows the English one-sheet, six-sheet, 12-sheet, and 24-sheet!
So now we know for sure that, after World War II, British Quads, English door panels, and English half-sheets were made for use in the "United Kingdom and Eire", and that English one-sheets, six-sheets, 12-sheets, and 24-sheets were made for use "overseas"!