This attribution is commonly made, but is almost certainly false. The original story was probably fictional.
To summarise the conclusions of The Quote Investigator: the first recorded telling of the story was in the Daily Times of Oswego, New York, in November 1899. It concerned two anonymous people in a railway carriage, who are almost certainly fictional. Four months later, in March 1900, the American humourist Marshall Pinckney Wilder "claimed authorship of the gag".
The first attribution to Churchill (and an anonymous woman) was made in The New York Times in 1949. Nancy Astor's first credit was in The Glitter and the Gold, the 1952 autobiography of Consuelo Vanderbilt Balsan, who had been married to the 9th Duke of Marlborough – Winston Churchill's first cousin – from 1895 to 1921. There was, she wrote, "a strong antipathy" between Churchill and Astor.
In 1962 Groucho Marx wrote about the jest in his newspaper column, and he credited the punchline to George Bernard Shaw – the woman being an anonymous attendee at a lecture given by "the red–bearded literary giant".
"It is conceivable" (writes the Quote Investigator) "that Churchill employed this line, but he would have been knowingly or unknowingly re–enacting a joke that had been circulating for many years."
To which I would add that he would have needed a female stooge to set it up for him.
© Macclesfield Quiz League 2017