The Conservative housing minister Grant Schapps, and the shadow libraries minister Goloria de Piero, are both among the almost 700 members of the "Colonel Gaddafi Support Group".
Celebrities including John Cleese, Alan Titchmarsh and the Jewish comedian Sasha Baron Cohen are also falsely listed as backing the embattled Libyan dictator.
On learning he had been added to the group against his wishes, the broadcaster Andrew Neil, wrote on the wall: "How do I get out of this absurd group?
"Why is it possible you can be made a member without permission?"
The group was created by Claire Khaw, a BNP member and self-publicist who frequently aims to generate controversy online.
She yesterday rang BBC Radio 5's Victoria Derbyshire programme to tell the mother of a severely disabled six-year-old that she should have "rejected" her at birth to avoid burdening the taxpayer.
She was able to recruit Mr Neil and others to her pro-Gaddafi group because of a change to Facebook's groups system in October, which CEO Mark Zuckerberg said was "a fundamental shift" in the way people use the site. It now allows anyone on the site to add their "friends" to groups without their approval.
Dr Eamonn Butler, director of the Adam Smith Institute, an economics think tank, was surprised to find he was a member of the Colonel Gaddafi Support Group.
"Like many in public life I am quite generous about who I accept as a friend on Facebook," he said.
"I was astonished my name could be used in this way."
A spokeswoman for Facebook said there is no way for users to prevent themselves being added to groups by friends.
"We would always encourage people to only be friends with people you actually know," she said.
"When a friend adds you to a group, you'll get a notification right away and you can leave a group anytime."
In response to criticism from people she co-opted into her pro-Gaddafi group, Ms Khaw wrote: "I have just had enough with the IDIOTS here who can't even think themselves out of a ----ing paper bag.
"On the TOP RIGHT HAND corner of your screen is a button that you can click. It says LEAVE GROUP. Those who don't want to be here, click on that and ---- off."
There are long-established links between the Libyan regime and Britain's far-right. Nick Griffin, the BNP leader, then a member of the National Front, visited Tripoli in 1986 as a guest of Gaddafi to ask for funds.
Facebook said its groups policy is designed to be "similar to being involved in an email chain". In October, Michael Arrington, the founder of the technology blog Techcrunch, used the new system to sign up Mr Zuckerberg - who had accepted him as a friend - to a group promoting paedophilia.
EDIT This is an interesting read about Claire on Ben Woodmans blog