Writer Nick Redfern urged him to "consider making available for public scrutiny all of the many and varied UFO reports compiled by the government".
The request came as the government began to implement Freedom of Information (FOI requests).
Some 6,700 pages of UFO documents have been released by the National Archives.
Chelsea FC sighting
The documents also include details of a briefing made before a House of Lords debate on UFOs in 1979, and reveal that former prime minister John Major had been asked by a fellow MP in 1996 whether the government would set up a national inquiry into UFO sightings.
The declassified documents - from the MoD unit which investigated UFO claims from 1950 until it was shut down in 2009 - also include several sightings and investigations.
These include:
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A spate of sightings in west Wales in 1977 which included a hotel owner reportedly seeing two tall, silver-suited "faceless humanoids" which began making measurements
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A UFO sighting in Spalding, Lincolnshire, which led to the witness being visited by three tall men in black suits who "seemed to move silently"
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An RAF Air Commodore describing in a memo to Defence Intelligence Staff that he had seen a UFO flying above him when he was flying at 40,000 feet
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A mounted police officer seeing a "square/diamond shaped object moving across the sky and changing shape" whilst on duty at Chelsea FC ground in 1999
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A memo noting claims the naval task force sailing to liberate the Falklands in 1982 had been shadowed by UFOs - "presumably Little Green Men in ponchos"
Dr David Clarke, author of the book The UFO files and senior lecturer in journalism from Sheffield Hallam University, pushed to have these files released.
He said: "These records allow us to look behind the scenes of what must have been one of the strangest jobs in Whitehall."
'X Files' fiction
Files relating to the unit have been transferred to the National Archive since 2007.
The documents also include an email from an intelligence officer working on the desk who described the daily mechanics of the role.
The officer says it is not the MoD's role to confirm or deny the possibility of extraterrestrials, but to gauge whether unidentified objects are a threat to the UK's security.
In an email he says discussion of the unit "tends to suggest to the public that there are Top Secret teams of specialist scientists scurrying around the country in a real life version of the X-Files... [but] this is total fiction."
The files will be free to view for a month.
