With her androgynous beauty, Annie Lennox was pop's ultimate feminist icon. Now she's using her unmistakable voice to campaign for Africa's HIV/Aids victims. Here, she talks about Mandela, the anguish of romantic love – and why she might have been better off with a wife

Nobody could accuse Annie Lennox of having an excessive preoccupation with the trivial and frivolous. A few minutes after we sat down in the cramped bar of Notting Hill's Portobello Hotel, she was talking about death and injustice, systematic rape, torture and oppression. She also went on to reflect on her childhood nightmares about the Nazis, the suffering of starving children, her concern about global warming and the failure to find a peace agreement in the Middle East. At one point, she seemed to sum up her life outlook with the statement: "The world is a heartbreaking place, without any question."

If all of that makes her sound rather heavy and earnest, then I'm responsible for adding yet another injustice to history's multiplying toll. Because in spite of the solemnity of her subjects, Lennox is oddly warm and lively in conversation. She exudes energy and enthusiasm even as she describes a planet full of pain and despair. The effect is a little confusing, as though news of the impending apocalypse is being relayed by a Blue Peter presenter. But while she tends toward a bleak sensibility, she lacks the world-weariness of the cynic and the defeatism of a genuine miserablist. Instead there's an evangelic quality in those piercing blue-grey eyes and a vivacity in that wide-mouth smile that lends a passionate zeal to her pessimism.

At 55, she still retains the sleek figure and striking looks of her pop heyday, but her face is somehow softer, less guarded. The former Eurythmics singer has been nominated for the Barclays Woman of the Year Award, which according to the blurb "is given each year to an exceptional woman whose personal and public life has been both brave and bold. Such a woman is a modern maverick, combining extraordinary insight with determination and a visionary approach".

Words like "maverick", "bold" and "brave" were often used to describe Lennox's musical career, which was full of unorthodox moves and statements, but the nomination owes more to her work as a humanitarian campaigner, particularly in relation to Sing, the charity she set up to raise funds for and awareness of the prevention of HIV and Aids in South Africa, which has one of the world's highest rates of HIV prevalence. The charity works in liaison with Comic Relief, and the main beneficiary of its donations is a group called Treatment Action Campaign (TAC), which seeks to prevent mother-child transmissions. Sing has provided a £300,000 grant to TAC, which also aims to increase access to testing and treatment and improve education about HIV. Lennox also gives talks in support of her work, such as the "Why I am an HIV/Aids activist" lecture she delivered at the TEDGlobal conference in Oxford earlier this year.

There's little doubt that she does a commendable job, and one deserving of recognition. The one pedantic proviso, perhaps, is whether "maverick" and "brave" are the appropriate words to describe a western pop star supporting the fight against Aids. After all, among celebrities it's hardly an unusual or controversial cause. Certainly those working on, say, anti-malaria and anti-tuberculosis campaigns must look with envy at the charity galas, fashion shows, rock concerts and well-known faces that HIV/Aids activism generates?

"I can't make comments on what gets coverage," says Lennox. "It's all important at the end of the day and I can't cover it all. It depends on perspective. I was drawn to the issue because it was affecting women and children, so I identified with it. It was more an intuitive response than anything."

In 2003 she was invited to take part in the launch of Nelson Mandela's Aids charity 46664. At the time Mandela described Aids as a "genocide". Lennox later described her reaction to this event: "I see Nelson Mandela in the twilight of his years thinking: 'We've conquered apartheid – now Africans face genocide.' How can intelligent, educated westerners like myself live with that on my conscience? I know I can't."

Can a viral pandemic be classed as genocide? Genocide is not only about victimhood; it also concerns perpetrators. When I pick her up on the word, she says that it was Mandela's, not hers, although she accepts that it served to galvanise her. "And I think – I don't know, I can only assume – that he was referring to the wilful refusal of the government of [former South African president, Thabo] Mbeki to really address the issue in a properly effective way."

Regardless of her motivations, she has made and does make a difference. There are children who are alive today as a result of her work who would otherwise almost certainly be dead. Still, some of her pronouncements can appear ill-thought out or contradictory, and Lennox is not shy of making pronouncements. She maintains a blog on her website in which she frequently vents her frustration and rage at the world's wrongs. For example, last month she laid into "western consumerist culture", which some might find a little rich from a super-wealthy pop star who's sold more than 80m records. Similarly, she wants to halt global warming, but is opposed to nuclear energy, the resource that many experts agree is needed to replace fossil fuels. When I raise these points, she leans back with an anguished smile and says: "Please don't ask me for the actual answer to anything, because I don't have it. Because all I do is look at stuff and ask questions. What can I say? I just think the world's barking mad. Look, I'm not an expert. I'm just an ordinary person."

The truth is, though, she's not an ordinary person. She's a world-famous multimillionaire and people, especially her fans, take notice of her. What's more, she doesn't just ask questions, she also makes plenty of assertions. I push her a little further. "At the end of the day, everything is extremely complex. I guess I'm an idealist… I don't have clear-cut positions. I get baffled by things. I have viewpoints. Sometimes they change."

Unlike many outspoken people, especially famous ones, she's not particularly combative or egotistical in debate. She has the ability and willingness to laugh at herself, yet strangely her interviews often read as humourless. "You don't see the self-deprecation or wryness," she says, perhaps because it's delivered with a facial expression or vocal inflection rather than a rehearsed witty remark.

Nonetheless she says she enjoys the interview process. "Back on the couch!" she joked as we sat down. Her partner in the Eurythmics, Dave Stewart, once said of their time together in that band: "We were eight years in psychotherapy with journalists." What everyone wanted to know about was their relationship. They had been lovers when they formed a previous pop band, the Tourists, in the late 1970s. But they split up before the Eurythmics and, in Stewart's phrase, "took eight years to untangle… a complicated relationship".

Apart from anything else, their entanglement meant that neither was able to form a solid relationship with anyone else. She got married, briefly, to a German Hare Krishna monk. The story goes that he won her heart by leaving vegetarian dishes outside her room while she was on tour. The image of female strength that Lennox so emphatically projected on stage and in her videos was partly that: an image.

In her dyed-orange crop and men's business suits, she was a picture of slick modernity: cool, feisty and sharply composed. The androgyny inevitably raised questions about her sexuality. "I didn't want to be perceived as a girly girl on stage. It was a kind of slightly subversive statement and what's even more subversive about it is that I'm so not gay. I'm completely heterosexual."

With the indomitable persona and that potent voice – a distinctive mix of gifted technique and tenacious delivery – Lennox became the pop diva as feminist icon. She was every strong woman's favourite strong woman. Behind the scenes it was a less empowering story.

"It was tough, really tough," she says. "When I look back it was almost like a lost decade in terms of my emotional life. It was a mess. I was not in a good space. I was very, very isolated."

She was not suited to touring, essentially, she thinks, because in spite of the men's suits she was not a man.

"I think life on the road really suits very egotistical men. It's set up for kings."

But Lennox couldn't or didn't want to throw herself into the traditional tour pastimes of sex and drugs and mayhem.

"It wasn't my scene. It was like the party was going on in the other room. It would be almost embarrassing if you looked at my rider: a few bottles of water, some raw ginger, some honey and tea, some raw vegetables, and that's about it."

You can see how the Hare Krishna monk might have seemed like an attractive option. But, notwithstanding his culinary talents, the monk didn't last long. The civilian husband to a female superstar has never been the easiest or most enduring of positions.

"I didn't know I needed a wife," says Lennox, half-jokingly, of her peripatetic life in the 1980s. "I would have been perfect as a man. That's your headline. There we go. Just because my life was set up for it and I didn't realise. It's tricky. It's about roles. If you're in a position where you're perceived to be powerful…" she trails off without completing the observation. "Actually, I'm quite a domesticated person. I love the little things of home."

It was to home that Lennox headed when she met her second husband, the Israeli film producer Uri Fruchtman. In December 1988 their first child, Daniel, was stillborn. The death marked the beginning of Lennox's withdrawal from the celebrity frontline. The next Eurythmics tour was her last, the band split up, and Lennox devoted herself to the two daughters she went on to have with Fruchtman.

She'd had her fill of fame, and remains scathing about celebrity culture that has mushroomed in the decades since. "People who want to get into this business because they want to be famous," she says, "haven't got a clue what they're talking about. Do something that warrants interest in what you're doing, and then try living with the fame because, actually, that is a bit challenging."

She talks about the invasions and intrusions that come with fame, not to gain sympathy but simply to give a lie to the glamour. "When I lost my first baby, I experienced a taste of just how low people can go. You know, I'd lost a baby and people were trying to get into the hospital to get interviews. That's disgusting. It was just loathsome. I said to myself: 'I'm going to protect this family of mine. I'm not having this life.' Having said that, I got off lightly. Back in the late 1980s there wasn't digital downloading of images that are sent instantly round the internet. There was a picture of Russell Brand the other day; apparently he punched a photographer. I don't effing blame him for taking a pop at that lowlife," she says in a manner to suggest that she wouldn't have minded adding a few pops herself. "He's living in the spotlight there, and I wouldn't want that life for anything."

All the same, she briefly reformed Eurythmics with Stewart in 1999. Whether or not by coincidence, her marriage to Fruchtman ended the following year. Subsequently she's said that she's not built for marriage, and that she has serious doubts about the possibility of romantic love. "It's a fine thing if you can get it," she said, "but then if you're a person like me, it will take you to a place of anxiety, because it can never be sustained. We want it – but when we get it, it's terrifying because you could be hurt, abandoned, and it's actually a really risky place to be."

You sense that Lennox has a tremendous emotional capacity but that it's bound up with an extreme sensitivity to the vagaries and frailties of life. She traces this feeling back to her childhood in Aberdeen. "I was perfectly safe and happy there," she says, "but when I think about it, when I go back, it was grim, you know." Even at a young age she realised that she was more than usually disturbed by mundane misfortune, "things like a dog being knocked down or seeing a dead bird".

"You become conscious when you're a kid that the world is a bad place," she says, and recalls the fear she went on to feel about the nuclear threat in the 1970s. Again, there's a strange disjunction between what she says and how she comes across. She may sound highly strung, but her demeanour is admirably grounded.

Still, while she doesn't put herself on a pedestal with regard to other people, her estimation of humanity appears not to be very high. Whether a despairing disposition has affected her view of the world or the state of the world has caused the despair is perhaps a philosophical distinction. The net effect is that making herself feel better has become almost synonymous with making the world better, so that hers is a kind of humanitarianism of the soul.

Sometimes this has led her into disputed territory. Last year, for example, she came under fire when she spoke out against Israel. "I was critical of Israel's policy of bombing Gaza," she explains, "that was populated by mainly children in a space where they couldn't escape from. I said that it was not the way forward to peace." However some felt that, in attending the demonstration against Israel, she was effectively supporting the Palestinian Islamists, Hamas, a suggestion she flatly rejected. Even so, she was accused of naivety and even antisemitism.

"That really hurt," she says now, "and it's a pack of nonsense. My children are half-Israeli. Why should I ever be antisemitic?" Her Israeli ex-husband, she says, respected her stand and told her there were many Israelis who were proud of her.

I wondered if she had been to Israel recently.

"No, not for years. I don't have any interest to go to Israel. I don't think I'd ever have a cause to go. It would be too volatile [to perform], I think, because people get carried away and they twist what you say."

Despite that experience, she remains committed to speaking out against what she sees as injustice. And she has no time for pulling punches out of cultural sensitivity. "I think the stoning of women is barbarous," she says, "and I think genital mutilation is barbarous. I will talk about these things because it's about my gender."

We come to the end of our time and, when her PR man enters, she repeats the comment that, she thinks, will be the one that stands out. "I would have been a fantastic man," she tells him and laughs out loud again.

Perhaps she would have made a fantastic man. But all things considered, it has to be said that she's done a pretty remarkable job as a woman.

The Barclays Women of the Year Award is announced on 11 October (womenoftheyear.co.uk). Annie Lennox's single "Universal Child" is available to download from 12 October, and her new album A Christmas Cornucopia is released on 15 November