He feared if word got out it would provoke "mass panic".
And the claim, made by a scientist who said his grandfather was one of Churchill's bodyguards, is recounted in secret files released by the Ministry of Defence.
The new reports detail four cases which remain unsolved despite the Government deploying RAF planes to investigate.
They also reveal that Churchill was accused of covering up a close encounter between an RAF aircraft and a UFO during World War Two.
He allegedly ordered that the unexplained incident over the east coast of England should be kept secret for at least 50 years because it would provoke "mass panic".
Alien expert and former MoD man Nick Pope has labelled the latest reports, which prove aliens are really out there, as "fascinating" and added: "They're as wonderful as the fictional X Files."
Also detailed in the 18 files, dated 1995-2000, are a near miss between a UFO and a Boeing 737.
Both the pilot and the first officer saw it but no explanation as to what it was was ever found.
There is also a case of a psychic warning of a bomb attack and a gambler who appealed for the Government's help after Ladbrokes would not pay out on his 100-1 bet that aliens would land on Earth.
Pope added: "Most of these sightings were misidentifications of things like aircraft lights or meteors, but a small proportion could not be explained.
"It shows the MoD's UFO project looked at anything weird and wonderful."
The files can be accessed at nationalarchives.gov.uk/ufos and will be free to view for the first month.Therealworldno.blogspot.com
