Ex_Mil8 saidI've watched the footage and - while it is slightly embarrassing in light of subsequent events - it's not exactly Nuremberg rally stuff. Princess Elizabeth (the current Queen) is first to throw up an arm, in what looks like a random gesture and the rest follow. It just looks like daft mimicking.
Of course, before WW2, there was a significant pro-fascist movement in Britain, but you have to see that in the context of the time. Many people in the interwar years believed it was going to be a straight choice between fascism or communism (the Cambridge spies, for example, chose communism).
The best thing would be for the Queen to open up the Royal Archives covering 1920-45 and allow historians to put these things into proper context. We already know The Duke of Windsor (formerly Edward VIII) had Nazi sympathies and many of Prince Philip's German relatives were Nazis (the Queen Mother was apparently disapproving of his 'hun' roots). None of this is news.
It was a gesture sweeping Europe in the early 1930s. Mussolini in Italy had created it in the 1920s, and Hitler in Germany borrowed it. I believe Franco in Spain also used it at times.
Its sinister associations weren't fully understood until a few years after these images of the Princess Elizabeth were taken. Elizabeth's uncle Edward, Prince of Wales at this time who's shown in these shots (and future King Edward VIII who soon abdicated, possibly under pressure from the government for his Nazi sympathies), may have stage-managed these poses.
In fact, Edward was so distrusted that Churchill, with Edward's brother King George V!'s approval, effectively exiled him to be the Governor of Bermuda during WWII. Edward, Duke of Windsor, would have preferred to stay in his residence in Vichy France, where he could keep socializing with his Nazi friends.
But the British government convinced him he was a hostage risk. And they promptly bundled him off to remote Bermuda, where he could do little harm, and have no influence.