The Queen rarely gives televised interviews, but the programme comes amid a revolution of the monarchy over the past 12 months, whereby the younger senior royal members have made regular TV appearances and her grandson Prince Harry is set to Wednesday actress and divorcee Meghan Markle, who is older than him and a woman of colour.
She also said the golden ceremonial carriage used for her coronation was "horrible".
She told presenter and Royal commentator Alastair Bruce it was "very heavy" - 2lb 5oz, to be exact.
In Graham's autobiography, Just As I Am, the man of faith wrote, "No one in Britain has been more cordial toward us than Her Majesty Queen Elizabeth II". "But once you put it on, it stays; I mean it just remains on".
The Queen rides in the Gold State Coach after her coronation
"So there are some disadvantages to crowns, but otherwise they're quite important things", she added.
The Imperial State Crown was made for George VI's Coronation in 1937 and is set with 2,868 diamonds including 17 sapphires, 11 emeralds and hundreds of pearls, including four known as Queen Elizabeth I's earrings.
The documentary also features informal footage taken behind the scenes, including images of son and heir Prince Charles, then aged four, and his younger sister Anne playing underneath the queen's long robe.
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She revealed the seven-metre-long (24ft) gilded carriage, which weighs nearly four tons and is pulled by eight horses, is "not meant for travelling in at all".
The sovereign said she had to keep her head still. The Queen said the crown had been "very unwieldy" when her father wore it.
This year saw a scaled-back State opening of Parliament Ceremony with the Queen arriving by vehicle rather than carriage and not wearing the Imperial State Crown or the Robes of State.
Bruce discusses the crown jewels with Queen Elizabeth in an exceptionally rare conversation recorded for television.
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If she has never officially given an interview, The Coronation is as close the Queen will ever come to displaying a hitherto unseen chat-show persona.
"She talks very cleanly and with a clarity of memory that was a delight".
It is part of the Royal Collection season, in partnership between the BBC and Royal Collection Trust.
To see the full interview, watch The Coronation on BBC One at 8pm on Sunday.
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