Arrivals at the new GCHQ established the lodge
The child molester, who died last summer, presided over ceremonies and rituals from an ornate throne.
Harding was convicted of an indecent assault against four children aged eight and nine in 1958 and classified a Schedule-1 offender, which meant the offence remained on his criminal record all his life.
His name was also on a list of about 400 Pie members seized by police in 1984, the year the organisation disbanded.
The Sunday Express revealed earlier this month how Harding met MPs Cyril Smith and Leon Brittan in the 1980s when he ran a north London antiques store.
Thirty-five years ago he appeared alongside paedophile television presenter Jimmy Savile in a Christmas special of Jim’ll Fix It.
The lodge boasts of its Government Communications Headquarters heritage on its website.
“These are people trained to find out sensitive information and yet none of them had any idea of Keith’s background and past convictions.
“They even voted him the highest honour by making him Worshipful Master.
“Keith felt the Freemasons were somewhere he finally belonged, he called them his “brotherhood”.
“When he died last year, they arranged his funeral and made sure the ceremony started at midday because the time apparently has significance within Masonic ritual.”
Spies displaced from London and Bletchley Park in Buckinghamshire, where the German wartime Enigma code was cracked, set up the Mercurius Lodge in 1957.
It meets at the Grade IIlisted Cheltenham Masonic Hall, purpose-built in 1823.
Harding ran the Mechanical Music Museum 10 miles away in Northleach after moving from London in 1987.
In 2013, he organised a trip to the museum for Freemasons and their families.
A photograph shows Harding wearing a Masonic apron, collar and medals during a ceremony a couple of years ago.
The Mercurius Lodge last night declined to comment.
Detectives probing historical sexual abuse allegations revealed on Wednesday they are investigating 1,433 suspects, including 135 from the entertainment industry, 76 politicians, seven sportsmen and 43 from the music industry.
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