To anyone in Britain who still thinks of her Dad as a tyrant, IRA quartermaster extraordinaire, and all-round Mad Dog of the Middle East, Aisha Gaddafi would like to extend a cordial invite.

“Come to Libya, you are all most welcome,” she says, when asked about her father’s unique talent for planting thorns in the side of successive British governments. “I know what is said in Britain about my father, and most of it is just following a political agenda. So I would give the British people this invite: find out the real facts by coming and meeting us Libyans in person.”

First though, meet Aisha herself, the only girl among the eight children that Gaddafi has fathered in between his other duties as Brotherly Leader, self-appointed Saviour of Africa and Guide of the Revolution. Dubbed “The Claudia Schiffer of North Africa” in the Arab press for her striking good looks, the 33-year-old is arguably the most photogenic of Libya’s First Family, yet she is still very much a chip off the old block. A lawyer by training, her father’s regime is not the only contentious cause she has spoken up for over the years. In her youth, just like her Dad, she was a keen supporter of the IRA, and three years ago, she was on the legal team that defended that other controversial Arab leader, Saddam Hussein.

Her other passion, though, is promoting women’s rights in Libya, which is why she agreed last week to a no-holds-barred interview at her home, a huge, high-walled villa in a Tripoli suburb. At first, it feels rather like being in a Gaddafi version of a Hello! shoot. Flawlessly turned out in peach jacket, white trousers and designer jewellery, Aisha holds court in a vast drawing room decked out with family pictures, and later poses for photos on a huge, mermaid-shaped settee worthy of her father’s extravagant tastes. Meanwhile, her three young children wander in – one of whom, three-year-old Muammar, is named after Grandpa.

“People forget that as well as being a great leader, he is also my father,” she smiles, as the pint-sized Gaddafis scuttle about. “We are very close as a family, and while he is always very busy, every day I insist that we have a gathering with him. My boys love being in his tent, and they enjoy drinking his camel’s milk.”

This being the Gaddafi clan, though, our conversation soon strays beyond the cosy joys of domestic life and Aisha’s charity work. For while she may not be as well-known as her brother Saif, whose work in brokering his father’s detente with the West has made him the most recognised of the junior Gaddafis, she still has her own special place in the turbulent recent history of Anglo-Libyan relations. Back in 1986, when Margaret Thatcher allowed Ronald Reagan to use British airfields for bombing raids on Tripoli, she was in the Gaddafi family compound when a missile landed, killing her adopted sister, Hannah. TV footage reportedly caught Aisha, then aged just nine, shaking a small but furious fist at the world.

“It was a terrible night,” she said. “I woke up to the thunder of the bombs and the screams of my sisters, with blood spattered around me. But once I grew up, I learned that it was not Americans or British people who did this act, just their politicians.”

So has she forgiven Reagan and Thatcher? Just as Britons have been asked to forgive the Lockerbie bombing and the shooting of Wpc Yvonne Fletcher outside the Libyan embassy?

“What do you expect me to say? Thatcher really spoiled my childhood, and I will never forgive her, no. As for Reagan, that is the route of Allah, he went crazy and got Alzheimer’s. That is his punishment, I think.”

It is remarks such as these that have given Aisha a reputation as slightly feistier than her brother Saif, who has been openly critical of his father’s regime at times, and who is thought to have been influential in persuading him to end Libya’s years as a pariah state. She is similarly bullish about the Lockerbie bomber, Abdelbaset al Megrahi, whose release last year on health grounds has caused such furore in Britain. Unlike Reagan’s illness, she says, Megrahi’s cancer is not the result of divine intervention – although the fact that he has continued to stay alive might just be.

“We have always viewed him as a detainee, not a prisoner, as there is no evidence that he commited such a crime,” she says, adding that he deserves compensation for being locked up unjustly. “But it is terrible that there are politicians who are demanding to know why he is still alive. They have forgotten that it is an act of God. Nobody dies before his time.”

Lest any British reader now be reconsidering her invite to visit Libya, it should be pointed out that Aisha also has her softer side. Trained in criminal psychology as well as law, she is involved with a variety of Libyan charities promoting women’s rights, particularly in domestic violence and honour crimes. Western human rights groups say her personal intervention has helped in some cases, although they add that in a land that does not permit independent pressure groups, it is perhaps more akin to a medieval ruler granting pardons to lucky supplicants.

Nonetheless, last year she was appointed as a UN Goodwill Ambassador, in recognition of her work raising awareness of womens’ rights, poverty and HIV. She does, however, have her own unique views on who in the world is deserving of goodwill. In 2000, during a trip to London organised as part of Tony Blair’s charm offensive to Tripoli, she infuriated British diplomats by giving a talk at Speakers’ Corner in support of the IRA. And in 2004, a year after Blair finally persuaded Gaddafi to scrap his WMD programme, she joined the defence team for the trial of deposed Iraqi leader Saddam Hussein, “an elected president who was wrongly hung”.

“I feel duty bound to defend anyone wrongly accused,” she says. “Plus we should not forget that Saddam was a great supporter of the Middle East, and it was for that which he was charged.”

But was he not also charged, I ask, for killing nearly 300,000 of his own people? What about the Iraqis who wanted him dead too? “It is only normal that some people are against you and some are with you,” she says matter-of-factly.

What about the IRA, then, who received hundreds of tonnes of guns and Semtex from Libya during the 1980s, when the Colonel opened his armouries to any “freedom movements” who came asking. Should their British victims not get compensation, just as Tripoli belatedly paid compensation to the families of the Lockerbie victims? “Libya is not just some big saving box from which everyone can take money from,” she says, shaking her head.

At least, though, her answers about Libya’s past are clear. On the subject of the country’s future, it all becomes a little more vague. For most of her father’s 41-year-long rule, Libya has been run according to the diktats set out in his Green Book, a home-grown alternative to both capitalism and communism that his supporters sometimes liken to Tony Blair’s “Third Way”.

Instead of parliamentary democracy, which is seen as concentrating power in a few elected representatives, all policy is decided – in theory at least – by “peoples’ congresses”, who pass their wisdom from the bottom up. The one thing they seldom discuss, though, is the prospect of any kind of alternative government – a rule that applies to his offspring as well. When I ask Aisha if Libya might become a Western-style democracy, I am advised by her translator to rephrase myself the question more subtly – although even then, the answer comes back as another question.

“Which Western democracy do you mean?” she asks. “The ones that are supposed to be democratic, but which have secret prisons like Guantanamo? Our system is different – we have the peoples’ congresses, where everyone is in government.”

Still, has she detected any changes in her father? The West views him as one of history’s great chameleons, shifting from anti-imperial firebrand to ally in the War on Terror in the course of a decade. To Aisha, however, he remains steadfast, a “great school” from whom her own sons will learn,. “The man is the man,” she insists. “He never changes his principles, he believes in causes, defending the poor and underdog.”

All the same, with the Colonel now aged 68, the question of who will replace him one day can not be dodged forever. Despite Libya’s poor human rights record, few predict a democratic uprising. Its oil wealth means basic needs are catered for, and there is little sign of angry young students planning an Orange-style Revolution. Instead, power is expected to remain within the existing elite, although Saif is not the shoo-in heir that he is often seen as. Despite his diplomatic skills, he has no military background, a quality vital for keeping a grip on the country’s all-important security forces. Increasingly, another brother, Mutassim, a former Army colonel who now serves as Libya’s national security advisor, is tipped as the chosen one instead.

By that same might-equals-right criteria, Aisha, despite being the beauty of the bunch, is unlikely to replace her father’s face in the thousands of official Leader’s portraits all over Tripoli. But then again, perhaps she does not mind – the single most valuable piece of advice he has ever given her, apparently, “is the importance of being modest”.

With that, The Sunday Telegraph’s time Chez Gaddafi is up, although the hospitality is not quite finished yet. As we leave, a housekeeper bustles in with gifts: for my photographer and I, there are smart Gaddafi-style robes, and for my six-week-old daughter, there is a dummy in a special presentation box. It comes across as a genuinely thoughtful gesture, although as the large gates of her villa clang shut behind us, I wonder if I am falling for the same kind of charm tactics that so successfully wooed Mr Blair. Who knows – with Libya still trying to convince the world that it has changed its spots, perhaps Gaddafi’s girl might be a good choice as Leader after all.

Copyright Telegraph Media Group Ltd