German U-boats were patrolling the Atlantic to disrupt supplies being sent to Britain from the United States.
When the Laconia was hit, there were 2,725 people on board: 463 officers and crew, 286 British military personnel, 103 Polish guards, 80 civilians - mainly women and children - and 1,793 Italian prisoners of war.
However, as the ship went down, the German U-boat captain Werner Hartenstein immediately ordered the rescue of as many survivors as possible, taking 200 people on board, with another 200 in lifeboats behind.
A short time later, an American aircraft spotted the U-boat and launched an attack. Many of those rescued by the Germans died.
1,104 survived the incident.
As a result of this episode, U-boat commanders were instructed not to rescue survivors in future as it jeopardised the safety of German crews.
The story of the Battle of the Atlantic is told at the Merseyside Maritime Museum in Liverpool.
The Laconia was fitted with eight six-inch guns
The museum's Stephen Guy explained that most of the U-boat commanders were not Nazis.
"They were professional sailors," he said. "They understood the problems with seafarers.
"They had compassion. The commander of this U-boat was not a Nazi fanatic. He tried to help these people."
Adding: "But as a result of this, Admiral Doenitz, head of the German navy, changed policy.
"He issued an order not to save people, because the rescue had made the U-boat a sitting duck."
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