The footage shows Paul McCartney, along with his brother Michael, and John Lennon on a rooftop at their home, according to The Hollywood Reporter.
Contacted by the Liverpool Echo, Michael said he believed it was him, Paul and very likely Lennon.
"Wow! That could definitely be us. It was a really big occasion in Liverpool and that's what we used to do every summer -- take deck chairs and climb onto the concrete shed and watch a free show.
"And I think there is every chance John would have been there that year - absolutely. His friend, Pete Shotton, was a police cadet. And George could easily have been there, too. It's bloody mad - absolutely fascinating and unbelievable!" Michael said.
The complete film runs about 41 minutes and is available on YouTube. The glimpse of The Beatles comes at the counter of 34:33.
The Barry Miles-Paul McCartney book "Many Years From Now" had references to the fact that the McCartney brothers would watch the police training annually.
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