The terrifying plot came to light in a letter from British atomic expert William Penney warning the authorities of a possible attack in 1954, the Daily Express reported.
The documents are part of a series of classified letters from the 1950s released by the National Archives.
In a note to Atomic Energy Authority chairman Edwin Plowden, Penney told how Moscow was plotting to drop just a handful of the deadly weapons across London, causing "complete destruction" over a three-mile radius.
"Most serious risk of all -- fire storm," Penney said in the letter.
Penney, who died in 1991 aged 81, even accompanied his handwritten letter with a drawing of the resulting fall-out.
In the sketch, he drew circles where each of the warheads and the fallout would strike.
Each would be more powerful than the nuclear bomb that was dropped on Nagasaki in 1945, effectively ending World War II.
"Instead of using, say, 32 bombs on London, they would probably use three, four or five very powerful ones which would give the same total damage but need not be aimed accurately," he wrote.
The decision by US President Harry Truman to drop two atomic bombs on Hiroshima and Nagasaki saw the death of at least 129,000 civilians, many of whom were women and children, with more dying of radiation-related illnesses in later years.
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