It is thought the future King George VI, the Queen's father, was behind the camera.
The footage is understood to be part of a vast collection of photographs, correspondence and home movies that make up the royal archive, housed in the Round Tower at Windsor Castle.
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The Sun has refused to disclose the source but said "the original film remains under lock and key". It added that "several copies of the clip were made several years ago" and it had been handed one copy.
Senior sources told the Sunday Telegraph it was inconceivable that anybody working in the royal archive would have leaked such material because of their "loyalty" to the royal family. Outside access to the archive is "rare" and "tightly controlled".
Film-makers make requests for access to home movie footage for documentaries including tribute programmes.
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