The letters span 63 years and begin with passionate love letters from the future prime minister, then mature into an affectionate correspondence between friends before, during and after the war.
Christie's auction house announced an anonymous bidder paid 77,675 pounds, more than three times its estimate, for a letter dated 6 March 1899, posted from Calcutta in then British-ruled India.
After Plowden's father Sir Trevor Chichele-Plowden had refused Churchill his daughter's hand in marriage, the future British leader wrote to her: "Were I a dreamer of dreams... I would say... marry me and I conquer the world and lay it at your feet... for marriage two conditions are necessary: money and consentment of both parties. One certainly, both probably are absent."
Meanwhile, a letter of condolence sent to Plowden after her second son was killed in action during World War II fetched 62,140 pounds - more than twice its estimate.
"Were I a dreamer of dreams... I would say... marry me and I conquer the world and lay it at your feet... for marriage two conditions are necessary: money and consentment of both parties. One certainly, both probably are absent"
Winston Churchill in a letter to Pamela Plowden
The correspondence, dated 19 July 1942 said: "My heart bleeds for you... both your gallant and splendid sons... have given their lives... heroes have not given their lives without a purpose being fulfilled."
Churchill met Plowden, a renowned society beauty in Hyderabad, India, when he was in his early twenties, and it is thought that they were informally engaged.
But she went on to marry Victor, Earl of Lytton, the son of a viceroy of India.
In a separate Christie's auction in London late on Tuesday, the
hearse used in Churchill's state funeral was sold for 5875 pounds, organisers said.