The documentary also revealed that numerous Crown Jewels were buried in a biscuit tin on the grounds of Windsor Castle during World War Two, to protect them from the Nazis - information that was so top-secret, the Queen herself only just found out about it.
One of the scenes shows the Queen describing the crown, which weighs nearly 22 pounds as "very unwieldy", to which Bruce adds: "It's hard to always remember that diamonds are stones and so they're very heavy".
The precious stones from the crown were put into a Bath Oliver tin and buried in a deep hole near a security entrance to the castle on orders from King George VI, reported The Times of London. Because if you did [look down] your neck would break, it would fall off.
The Imperial State Crown includes sapphires belonging to St Edward the Confessor and Alexander II of Scotland, a ruby from Edward the Black Prince, pearls from Elizabeth I and the Cullinan II diamond.
In the documentary, the Queen also talks about the amusing trials and tribulations of being head of state - from the perils of wearing a heavy crown, to her robes sticking to a thick carpet pile.
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"It's the sort of, I suppose, the beginning of one's life, really, as a sovereign", she said.
"There are some disadvantages to crowns but otherwise they are quite important things".
In a rare on-air interview, the queen recounts her 1953 coronation with remarkable candor. "I mean it just remains on", she said.
It also features a gemstone known as the Black Prince's Ruby, believed to have been worn by Henry V in his helmet at the Battle of Agincourt in 1415. She recalled the Coronation journey from the palace to Westminster Abbey.
The Coronation is part of the Royal Collection Season on BBC and will air this Sunday.
According to UK's The Telegraph, the footage is shown as part of an hour-long BBC One documentary "The Coronation" which airs in the United Kingdom this weekend and features behind-the-scenes footage of the Queen, capturing her sense of humor and life in the palace.