To her supporters, Mrs Rajavi, 43, is the President-elect of a post-theocratic, democratic Iran - the leader, along with her husband, of the only serious resistance to the fundamentalist regime in Tehran. According to the French authorities, the Iranian regime recently paid her the compliment of plotting to blow her to pieces in her place of exile, a village just outside Paris (shades of Ayatollah Khomeini).
To her detractors, including many other exiled Iranians and most Western governments, Mrs Rajavi is the figurehead of a deeply suspect, even sinister, organisation, the People's Mujahedin of Iran. Despite a plausible veneer of democracy and efficient public relations, critics claim the internal workings of the Mujahedin - and its political wing the National Resistance Council - are as brutal and repressive as anything dreamed up by the Ayatollah and his successors.
"Their background is a kind of anti-Western, Islamic Marxism. She is not as cuddly as she seems," said one Western expert on Iran.
Tonight Mrs Rajavi will make her first public appearance in Britain at an event at Earls Court in London, which is mostly cultural, but finally political. The event, entitled "Women, Voice of the Oppressed", is billed as a response to the persecution and repression of women by the fundamentalist brand of Islam popularised in Tehran. More than 20,000 people, including many Iranian exiles, are expected to attend. One of the performers will be the celebrated Iranian diva, Marzieh, who fled Iran two years ago after refusing to sing for 15 years in protest against the rule of the mullahs.
The Earls Court gathering is an attempt by the Iranian resistance to play to what it hopes is one of its strengths. Mrs Rajavi, in her interview with the Independent, said: "We wish to show that Islam is not, in itself, misogynist. There can be a moderate Islam which respects women's rights and gives women, as our movement does, a prominent role."
The promotion of women within the ranks of the Mujahedin extends to their military wing, a sizeable, armoured force, based, courtesy of Saddam Hussein, on the Iran-Iraq border. Many tank commanders, even battalion commanders, are women. The overall military commander, based in the desert, is Massoud Rajavi, Mrs Rajavi's husband. Despite her status as President-elect, Western governments insist that he is the real power in a movement they regard with deep distaste.
Here is a seeming paradox: the Iranian government is one of the most reviled in the world; the Mujahedin are by far the best funded, and best organised, certainly the most visible opposition to that regime And yet they are almost equally reviled by the powers-that-be in the West. The Iraqi connections are one explanation - but not a complete explanation - for Western hostility. How does Mrs Rajavi account for it?
She giggles patiently and shapes her hands into a triangle. "You know, there is a misconception that Western governments oppose the Iranian regime," she said. "The fact of the matter is that the mullahs in Iran possess so much commercial weight and Western businesses are so keen to reach deals with them that no government can make a statement of support for the Iranian resistance."
She points out (accurately) that the official investigation into the Iran-Contra scandal showed that the Reagan administration had agreed to vilify her movement as part of Washington's complex and disastrous series of quid pro quos with Tehran. The same sort of understanding with the mullahs exists to this day, she says.
"One of our demands has been that, if Western countries are not prepared to assist the revolution of the Iranian people, at least they should remain neutral. In those circumstances, it would not take long for the Iranian people and our movement to, if you like, settle the account and rid the world of the growing menace from Iran."
But what of the equally deep suspicions of many exiled Iranians? The hostility of royalists is understandable: the Mujahedin were co-conspirators with the mullahs against the Shah. They played a part in the popular revolution which overturned the peacock throne in 1978-79, before their turn came to be crushed by Khomeini in 1981. But what of the many virulent, non- royalist opponents of the mullahs who also express antagonism to the Mujahedin? One Iranian said: "If there was any threat of them coming to power, most sensible Iranian exiles would take the side of the mullahs against them. We would be just swapping one tyranny for another and Mujahedin tyranny would probably be more efficient."
Asked about this, Mrs Rajavi becomes animated, even angry. "I think one has to ask, who are these Iranians? Many of these people, despite what they say, prefer the status quo - the Khomeini regime - to any alternative. There are others who are afraid. There are many proven cases of threats against these people to make these criticisms of us . . . Everyone says we are well-organised, well-funded. But you have to remember that cannot happen in a vacuum. Our strength and our funds come from the deep roots we have in the people of Iran, both inside and outside the country."
Mrs Rajavi signals to one of her smartly dark-suited male colleagues to bring forward an album showing scores of examples of pro-Mujahedin slogans and posters on walls inside Iran. She insists that the critics are wrong: her movement is not Marxist or authoritarian. It is committed to free markets, free expression, freedom of religion.
"The model of the kind of society and economy I would like to see in Iran would be that of the Nordic countries. We would expect an open society where economic and personal diversity would prosper."
How long will it be before the second Iranian revolution comes? Mrs Rajavi smiles sweetly. She offers no timetable but gives what she admits is a practised reply. "One does not need to wait for spring to arrive to be sure that spring will come."