IF YOU GO DOWN TO the British Museum tonight you’ll be sure of a big surprise. A local hotel is hosting one of London’s most extraordinary Christmas parties. Among those who have been invited to feast on mulled wine and “seasonal canapés” are Jonathan Dimbleby, Fiona Shaw, Peter Tatchell, Chris Woodhead, Alan Sillitoe, Charles Moore, Fay Weldon, and Lord Evans of Temple Guiting. It is an eclectic mix, even by Bloomsbury’s standards, and an even odder one if, among the coincidence of faces, you notice a selection of backroom ideologues from the Left and Right, people not normally seen dead in one other’s company, still less drunk in it.

Their hostess is Claire Fox, director of the unlikely sounding Institute of Ideas. Every contradiction of the guest list is contained in this woman: a veteran of the Left but the Right’s latest pin-up; a professed socialist who speaks up for globalisation; the loser of a major libel action brought by one of Britain’s largest news organisations yet a media favourite, resident on Radio 4’s The Moral Maze and increasingly a participant on TV shows such as Question Time; a courteous and humorous social animal yet the possessor of views that cause phone-in hosts as well as their callers to abuse her on air, as when she set about defending Gary Glitter’s right to feast on child pornography.

In public debates, and she seems to go to them all, she says the unsayable. Over the last few years, I have noticed, however, that audience reaction to her has matured from “who the hell does she think she is?” to, more simply, “who is she?”

Others ask what on earth is the Institute of Ideas? Its website provides an anodyne self-definition. Its mission is to “expand boundaries of public debate by organising conferences, discussions and salons, and publishing written conversations and exchanges”. Co-sponsors have included the Royal Society of Arts, the Tate, the Royal Shakespeare Company and the British Museum. Two festivals ago, I spoke at an IoI session in Edinburgh on the future of satire. It was lively, fun and unpartisan.

The IoI’s origins lie, however, deep in a Seventies Trotskyite splinter group called the Revolutionary Communist Party and in its organ, Living Marxism. When the RCP abolished itself in 1996, Fox relaunched the magazine as the glossier, trendier LM. It was a minor publishing phenomenon until March 2000 when ITN forced its closure by winning a court case against it for an article that claimed it had misrepresented footage of an emaciated Bosnian Muslim at a Serbian internment camp. Some then accused Fox or being a pro-Serb “tanky”. The complaint now is different: that the IoI has mutated in a sinister fashion into a front organization for the far Right.

We meet at noon in the IoI’s narrow, white offices near Smithfield. Fox, wearing more make-up and looking more nervous than is usual for her, leads me out to a café which I say is too noisy. We move on to a delicatessen, Fox accusing me of being picky and “posh”. I say it just shows how unreliable impressions can be.

“I’m a little bit of an unknown quantity myself,” she says, explaining her nervousness. “I didn’t emerge in the traditional fashion. I didn’t come out of the Oxbridge club. I didn’t come out of the traditional trade union movement. I’ve just emerged on the scene and people are a little bit like, ‘What’s she about?’ ”

So what, I ask, is her agenda? She says they — she means IoI’s four staff — remain influenced by their left-wing background. She still opposes capitalism, although she stopped believing in revolution when the Berlin Wall fell.

Why, then, does The Guardian, which mounted a big investigation into the IoI two years ago, think her part of the American libertarian Right? “I’ve no idea why The Guardian think what they think, but there are people who seem to imagine that you can’t have an idea unless it’s paid for.

“The only explanation that some people can come up with for, for example, why I’m a relatively enthusiastic supporter of GM (genetically modified) food must be that I’m in the pay of the multinationals. It couldn’t possibly be that I have intellectually decided, having looked at the evidence, that GM might be a way of solving some of the problems of the developing world, might be at least something that should be looked at.

“It’s as though nobody believes any ideas any more. You must only have them because you’ve been bought off.”

When it comes to her defining her current principles, Fox talks vaguely about “challenging orthodoxies” and promoting “the idea of the active subject”. “We can make our destinies. We are not victims of it,” she says, and we segue into a conversation about how victimhood has become the new heroism and how Diana, Princess of Wales, has become its icon.

“The espousal of Princess Diana as a model is a disaster and, as one of the BBC’s Great Britons, a complete disaster. She’s a great Briton because she suffered more than anyone else and she talked about it and opened her heart.”

The Sexual Offences Act currently before Parliament is another symptom of society’s search for victims. “Its notion of consent is extremely dangerous. The idea that you have to ask for consent, that is that consent has to be explicitly given, would indicate that this was drawn up by people who have never had a sexual encounter, never had a personal encounter and have no idea about how human beings work. Either people will stop having sex, which won’t happen, or more and more people are going to be done for rapes when I do not think rape will have occurred.”

But the “there was yes-yes in her eyes” defence is pretty scummy, isn’t it? “Look, human beings have to be treated as grown ups who can actually negotiate these things. I’m not saying there aren’t times when the law and people’s defences can be irritating. But even this encounter, it’s not unambiguous. Life is not unambiguous. I mean by that: ‘am I being set up?’

Not am I going to pounce? “No,” she says, “but it’s nerve racking. There’s a degree of risk. But I have to be a grown up. You have to be a grown up. We have to trust each other to a degree and maybe that trust will be abused and that won’t be the end of the world either. We’ll both survive.”