Princess Elizabeth was named Colonel of the Grenadier Guards on her sixteenth birthday, April 21, 1942. That day, she conducted her first official engagement, an inspection of the regiment at Windsor Castle, in a military-styled hat with visor and pleated halo crown.
She would wear a another version of this hat several times during the final years of WWII, along with the similarly styled cap of her Auxiliary Territory Service uniform.
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Image from Getty as indicated
Royal Hats 
Yesterday, I mused about the possibility of Margaret getting Elizabeth’s cast-offs as a part of the war effort. PLEASE say that the following photo proves me correct, with Margaret in 1944 wearing her sister’s 1942 16th birthday hat, without the central clip/brooch.
January 31, 1944
https://outlet.historicimages.com/products/rsd04137
Just for fun: Very nice in blue.
https://pxpuzzles.com/featured/princess-elizabeth-ii-william-timym-circa-1944-war-is-hell-store.html?product=puzzle&puzzleType=puzzle-18-24
Looks like it to me! Very well spotted, as always!
It isn’t surprising that this is the hat we associate with the then-Princess Elizabeth in the war; one thing the Royal Family felt they needed to do and were good at was setting an example / not being given special privileges, and clothing was rationed, so she probably didn’t own many hats!
I’m intrigued by the picture with her grandmother, as Queen Mary’s hat is such a plain style that it seems difficult to reconcile with her wearing it! Perhaps more wartime influence.
Such a distinctive style worn by Princess Elizabeth during the years of World War II.