The script, written in 1983 amid fears Britain would be attacked by the Soviet Union, is part of a bundle of government documents released by the National Archives.
In sombre tones, it says the country faces the "madness of war" and must prepare itself "to survive against great odds".
"When I spoke to you less than three months ago, we were all enjoying the warmth and fellowship of a family Christmas," the Queen would have told the nation.
"Our thoughts were concentrated on the strong links that bind each generation to the ones that came before and those that will follow.
"The horrors of war could not have seemed more remote as my family and I shared our Christmas joy with the growing family of the Commonwealth.
"Now this madness of war is once more spreading through the world and our brave country must again prepare itself to survive against great odds."
The speech, which was never read or even seen by the Queen, was prepared as part of a Whitehall exercise known as Wintex-Cimex 83, designed to work through potential scenarios in the event of nuclear war.
It refers to the Queen's "beloved son Andrew", serving with his unit as a Royal Navy helicopter pilot at the time, and the address by her father George VI on the outbreak of the Second World War.
It adds: "We all know the dangers facing us today are greater by far than at any time in our long history.
"The enemy is not the soldier with his rifle, nor the airman prowling the skies above our cities and towns, but the deadly power of abused technology.
"But whatever terrors lie in wait for us all, the qualities that have helped to keep our freedom intact twice already during this sad century will once more be our strength.
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"My husband and I share with families up and down the land the fear we feel for sons and daughters, husbands and brothers who have left our side to serve their country.
"It is this close bond of family life that must be our greatest defence against the unknown.
"If families remain united and resolute, giving shelter to those living alone and unprotected, our country's will to survive cannot be broken."
The text was drawn up during one of the most dangerous years of the entire Cold War.
US President Ronald Reagan had denounced the Soviet Union as an "evil empire", while the shooting down of a South Korean airliner when it strayed into Soviet air space, killing all 269 people on board, further ratcheted up tensions.
A Nato military exercise, codenamed Able Archer, nearly triggered an actual conflict, with the Soviet leadership apparently convinced it was cover for a genuine attack.
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