The Jelly Bean update for the Galaxy S III is steadily spreading to more countries in Europe, in addition to Poland, Sweden, France, Spain, Romania, and Austria. Today, it started rolling out in Italy (H3G), United Kingdom (H3G), Switzerland (Swisscom), and Ireland (Three), as well as on another Austrian carrier called 3 Austria. As far as I can tell, H3G, Three, and 3 are all owned by the same giant company - Hutchison Whampoa (some names are even interchangeable), so four out of five pushes today seem to be a coordinated effort.
Curiously, the majority of the updates (those pushed by Hutchinson-owned carriers) are no longer I9300XXDLIH dated September 28, but rather I9300XXDLJ1 which is a fresher build dated October 8. As before, if you don't get an OTA prompt, you can try to hook up your S III to Kies and check there, or download the full ROMs at either SamMobile or Samsung-Updates (neither site is officially endorsed by Samsung, in case there is any confusion about their nature).
Thanks again, Adam!