Thankfully, that didn't happen. But it could have. In any case, the Queen was ready with a speech, drafted by the British government, to urge Britons to remain united and resolute against "the madness" of nuclear war:
The document, released by the government under the 30-year rule, was drawn up as part of a war-gaming exercise in the spring of 1983, which worked through potential scenarios. [...]
Although it was only a simulation, the text of the Queen's address - written as if broadcast at midday on Friday 4 March 1983 - seeks to prepare the country for the ordeal of World War III.
The script, which starts off by referring to the Queen's traditional Christmas address, reads: "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. [...]
"Not for a single moment did I imagine that this solemn and awful duty would one day fall to me.
"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." [...]
"If families remain united and resolute, giving shelter to those living alone and unprotected, our country's will to survive cannot be broken."
The speech concludes by saying the Queen's message to the nation was "simple".
It adds: "As we strive together to fight off the new evil, let us pray for our country and men of goodwill wherever they may be. God Bless you all.
Read the entire speech over at the BBC: Link