The British prime minister said the unexplained incident should be kept secret for 50 years, fearing it would provoke a "mass panic."
The claim was discovered in files newly unclassified by the British Ministry of Defense. It came from a scientist who said his grandfather was one of Churchill's bodyguards.
According to the documents, details of the coverup emerged when the man wrote to the government in 1999 seeking to find out more about the incident. He described how his grandfather, who served with the Royal Air Force (RAF) in the war, was present when Churchill and U.S. General Dwight Eisenhower discussed how to deal with the UFO encounter.
The man, who is not named in the files, said Churchill was reported to have exclaimed, "This event should be immediately classified since it would create mass panic amongst the general population -- and destroy one's belief in the church."
The incident allegedly involved an RAF reconnaissance plane returning from a mission in France or Germany toward the end of the war. It was over or near the English coastline when it was allegedly suddenly intercepted by a strange metallic object that matched the aircraft's course and speed for a time before accelerating away and disappearing.
The mysterious files also reveal a lengthy history of reported close encounters over the years.
In one incident, a gambler approached the Defense Department for help after a local gambling parlor refused to pay out on his 100-1 bet that aliens would land on Earth before the end of the 20th century.
And an alien spaceship "20 times the size of a football field" is among the string of bizarre UFO sightings. The huge craft was reported to the military after it was seen hovering above Manchester airport in January 1995. In another report, a black U-shaped object was seen from Edinburgh travelling above a Scottish river without disturbing the water on October 9, 1995.
During the Cold War, RAF jets were scrambled 200 times a year to investigate UFOs picked up on radar. But this fell to zero after the collapse of the Soviet Union in 1991.
Nick Pope, a former Ministry of Defense expert who worked on the official UFO files, told London paper The Sun, "Whatever you believe about UFOs, there's some fascinating material in these real life X-Files."
"Most of these sightings turned out to be misidentifications of things like aircraft lights or meteors, but a small proportion could not be explained."
The Sun contributed to this report.