That Hamilton Woman, its original British title was simply Lady Hamilton, is a 1941 historical film drama, produced & directed by Alexander Korda, for Alexander Korda Films.
It tells the story of Emma Hamilton, who was mistress to Admiral Horatio Nelson with these roles played by Vivien Leigh and Laurence Olivier. Heather Angel also appear in the film in a minor part of a street girl. The story start at the end of Lady Hamilton's Life, in the slums of Calais, and shows her life by means of a flash back.
Stars Vivien Leigh and Laurence Olivier were newlyweds at the time of filming and were considered a "dream couple".

Trivia
In Horatio Nelson's (Laurence Olivier) opening scene, he informs Lord Hamilton that he has received orders from Lord Admiral Hood, a role that Olivier would play 43 years later, in The Bounty
It was stated to be the favorite film of Sir Winston Churchill
Made in wartime, Napoleon was equated to Hitler and Nelson to 'Britain fighting on alone' in WWII.