I was flipping through a book on Rav Kook ("An Angel Among Men", by Simcha Raz), and came across something fascinating: A photo captioned "A letter from Herbert Samuel, the British High Commissioner, informing Rav Kook that King George V has decided to present the Rav with a medallion of honor".
The letter in the photo isn't clear*, but on the same page is another photo, showing Rav Kook wearing the "medallion" in question. The caption to that photo goes on to say, "Notice that it is partially covered, because of its cross shape." Indeed, a fold of Rav Kook's coat covers one arm of the cross**, but it's clear that it's an Order of the British Empire, probably a Commander's badge, based on the dark (in a black and white photo) ring at the center.
(Commander is the third of five levels. This badge might indicate a higher rank, in which case Rav Kook would be a Knight and thus "Sir Kook" if residents of Mandatory Palestine were British citizens or subjects- I don't know if they were.)
Anyway, I've searched, but can find nothing more on this. I'll admit I'm not the biggest student of Kook-studies, but does anyone else know?
*It's typed in Hebrew, signature in English. I can make out that it's dated June 11, 1922, and has words that would translate to "Order of the British Empire," ending with the word "BeYoter"- "high degree."
**Rav Kook is holding a book at the point where the coat folds over the cross. Is the fold inadvertent? Was he holding the book to cover up a deliberate fold? Is it possible an arm was broken (after all, a covered cross is still a cross) and he's covering that fact, not an actual arm?