The first time David Furnish went for an HIV test, in his early 20s, the procedure hadn't even been invented. The doctors could only test his immune system for stress, and as far as they could tell he was fine, but Furnish was so terrified of Aids, "I went back in the closet. I stopped having sex with men."

His mother had wept when, aged 21, he told her he was gay. A middle-class Canadian housewife, "She cried for a week. She said, 'You'll never have a family, you'll never have children of your own. And you might die of this disease killing all those gay men in New York and San Francisco.'" Furnish couldn't offer a single successful gay role model to reassure her, apart from Boy George. "And I love Boy George to death. But he didn't exactly give my mother the comfort she was looking for. So I thought, This is too terrifying, I cannot do this. I probably just need to find a loving girl and hope I can have a sexual connection with her." By the time he left Toronto for London in his late 20s, he was seeing a woman, secretly sleeping with a man, paranoid about being outed and hating himself for the dishonesty.

The last time Furnish had an HIV test, 12 days ago, he wanted the world to know about it. Elton John's husband invited news cameras into a hospital in east London to film a pilot scheme being promoted by the Elton John Aids Foundation, offering every outpatient arriving for a blood test an HIV test as well. At 51, Furnish has lived his adult life through the narrative of HIV/Aids, to the point where he could practically be a character in an Armistead Maupin novel. When he and John first met at a dinner party in 1993, the disease was a death sentence, Section 28 was on the statute book, and Furnish hadn't dared fully come out. The singer had just started his foundation, and both men had watched countless friends die.

Furnish came to most people's attention four years later, when he made a TV documentary about John, Tantrums & Tiaras, a startling portrait of his high-maintenance boyfriend whose monumental hissy fits were as jaw-dropping as his wardrobe. When a fan had the audacity to say hello while he was playing tennis at a hotel in the south of France, the singer demanded a private plane fly him home immediately, declaring he would never set foot in France again. But the documentary was also tender and touching, leaving viewers intrigued by this unassuming Canadian who had captured the star's narcissistic heart.

When they wed in 2005, on the day civil partnerships became legal, the couple were half expecting to be heckled by anti-gay protesters, but were instead deluged by congratulations from all over the world. They hadn't expected the ceremony to change their relationship; they thought they were just celebrating the breakthrough in gay rights. "But when the dust settled and we went away and we were in our little apartment in Venice on our post-Christmas break, we both looked at each other and felt this much greater sense of contentment than either of us had expected."

Today the couple live between their two American homes in Atlanta (it's apparently easier for John to tour from there) and Los Angeles, with their two children, two-year-old Zachary and 11-month-old Elijah. At 66, John is one of the most bankable live performers on the planet, and Furnish is a film and stage producer, responsible for the 3D animation Gnomeo & Juliet and Billy Elliot The Musical, but he still devotes at least one day a week to the foundation's work.

Having raised $300m (£183m) and witnessed astonishing medical advances, 20 years on the Elton John Aids Foundation operates in a world that two decades ago would have been unrecognisable. "It really is a miracle," Furnish says. A vaccine or cure may not yet be here, "but the drugs are now so effective, we can end Aids anyway". If you contract the virus today, and are diagnosed within three years and treated, your life expectancy is the same as everybody else's. "And you can actually now take antiretrovirals as a prophylactic. If you are HIV negative and take an antiretroviral every day, if you have unprotected sex with an HIV-positive person, you reduce your risk of contracting HIV by 99%." The drug, called Truvada, is relatively new and Furnish is surprised that the uptake has so far been slow.

Last week, Furnish left his family in Atlanta to spend the days leading up to World Aids Day in London talking to people infected by partners who'd been too frightened to tell them they were positive, or too fearful to get tested. Some described being ostracised by their families; one woman found out she was positive only when she became pregnant, and though her baby was safely delivered by caesarean, the maternity nurses refused to touch her. 

"It is horrendous. It's like going back to the 80s, when there was no treatment, when there was nothing at all. HIV isn't something people need to fear at all any more. But we're back to a situation where there is still so much stigma and ignorance, just because our attitudes haven't caught up yet. You can understand the stigma when you go up in the mountains in India, say. But then you come all the way back home to good old London, where you assume people are relatively well read and more sophisticated, and you hope more compassionate. And then you see what people go through. It's exactly the same here as it is in developing parts of the world, and it is really desperate."

On first impression, Furnish comes across as an unlikely activist. His grooming is so flawless, he looks as if he's been Photoshopped, and he has a sweetly modest, almost innocent demeanour. Before meeting John, he'd been in advertising, and talks in the smoothly polished voice of a transatlantic executive. But as soon as he talks about HIV, Furnish becomes very focused, the antithesis of a celebrity endorsing a cause he doesn't know much about.

"Everyone should be tested," he says. "Whenever they have a checkup, they should test for HIV, because if we can get to a point in our society where everyone is automatically tested, nobody will fall through the net. In strictly medical terms, there's no difference between HIV and diabetes; they're not curable, but they're very, very highly treatable, and early information is power. The only thing – literally the single only thing – that is different is the stigma. And we have to overcome it, because it is now the only reason people are dying."

Half of all new HIV cases in this country are contracted through heterosexual sex. In the general population, the odds of the next person you sleep with being HIV-positive is one in 650. If the next person you sleep with in Britain comes from Zimbabwe or Nigeria, the odds are one in 20. But it's within ethnic minority communities that the stigma remains most entrenched, and so the foundation is helping fund a project in London to persuade imams and pastors to talk to their congregations about HIV, and encourage them to be tested. 

There is an irony that the disease that once made any idea of fatherhood unthinkable, and was the cause of so much shame and terror, has ended up being the very thing that led Furnish to become a parent.

"I came from a happy family with loving parents, so my associations with marriage and children were all happy, positive things that brought me comfort as a child, which I wanted in my life." John, on the other hand, had grown up terrified of his own father, and always been clear he did not want to be one. But four years ago the couple visited Ukraine, where HIV is endemic and the foundation is busy, and visited an orphanage full almost entirely of children whose parents were either dying or dead from Aids. They met an HIV-positive boy called Lev, fell in love on the spot, and wondered if they could adopt him and his brother.

Furnish thinks they might have been able to, were it not for a random question at the end of a press conference later that day. Had the visit, a reporter asked, tempted John to reconsider adoption?

"Elton's often blissfully and sweetly unaware of the impact that he has with his celebrity, because he's not really a very self-centred person in that regard at all. So Elton just said, 'Well, we met this little boy called Lev today, and he's sitting on David's lap, and I don't know if it's possible or anything, but yes, we would be interested in adopting him.' And that just opened up such a can of worms, and it quickly turned into a bit of a three-ring circus. I actually think that had he not said that, we probably – well, there wouldn't have been such a negative public response within Ukraine to us adopting Lev and his brother."

Thrown by the global media frenzy, the Ukrainian authorities were having none of it. They do not recognise same-sex marriages, and after six fraught months of legal wrangling, the couple were forced to concede defeat. By then, a newspaper had tracked down the boys' mother, "plied her with a case of vodka", and taken her to the orphanage to see them – unaware that a child could not be eligible for adoption until it had spent a year there with no family visits. "So they basically set the boys' time clock back to zero." Advised by psychologists that after three years in an orphanage, the psychological damage would be irreversible, "We said, 'This is not about us, it's about them.' And we've got to get them out of the orphanage quickly." Lev and his brother now live with their grandmother, and contrary to many press reports, Furnish says he and John are still involved in their lives, but doesn't want to say how for fear of visiting any more media attention on the boys. 

The remarkable thing about Furnish is that, from the way he talks, you would think he had no idea that all over the world there are people saying nasty things about him, accusing the couple of treating babies like designer accessories. The impression of oblivion is so striking that, when we first met, I wondered if he was perhaps just not particularly bright. But it soon becomes clear that he is very smart, and knows exactly what people say. He's just one of those rare people temperamentally immune to provocation, and doesn't let it get to him.

His husband is, famously, a different kettle of fish. John has talked a lot in recent years about growing less volatile, though, and when I ask if that's true, Furnish laughs. "Elton is an artist, and as an artist he's wired differently from other people. He's incredibly passionate about what he does, and the energy of the passion may it never go away. I love that side of him, and I love how he continues to remain so passionately connected with our world. But the tantrums, the insecurity and the unreasonable behaviour we saw in Tantrums & Tiaras – yeah, that's pretty much faded away." He thinks the public acceptance of his husband's sexuality and their relationship has had a lot to do with John's ease in his own skin today. "He still gets angry about things he feels passionately about, and he's always one to express his opinion – and that's just part of who he is. But I love that side of him and I would never want that to change. I would never want him to suddenly stay at home on the sofa with the remote control and watch football all day."

When Lev's adoption failed, the couple were left with a gnawing sense of emptiness they hadn't anticipated or known before. By coincidence, at the time two of Furnish's friends in same-sex relationships were embarking on surrogacy. They'd not considered it before, but John's response was instant: "OK, let's do it."

Zachary will be three on Christmas Day and has already started asking questions about where he came from. The other day he asked his nanny if she was his mother, and when she said no, Furnish laughs, Zachary's response was, "Oh, OK, then you must be my girlfriend." He wants the boys to know "their creation is and was a very special thing, and that everybody who was part of it did it for the right reasons". Rather than decide which one of them would be the biological father, the couple left the genetic paternity to chance by opting to have their sperm mixed. The surrogate they chose is a mother of two who has carried five babies, donated eggs twice and "talks very articulately and passionately about how surrogacy gave great purpose and meaning to her life. When she was feeling kind of directionless, surrogacy sort of found her." She has written to both boys, telling them "what an amazing experience it was and a privilege for her to carry them", but the egg donor was chosen anonymously, based on "her really exceptionally healthy family history of health and longevity".

Furnish and John read the boys books about different types of families, and still can't tell which of them is either's biological son. "I've been told," he says, beginning to laugh, "it's the topic of conversation at a lot of dinner parties in London. The reality is, we don't know, and we're not bothered in the slightest." John is called Daddy and Furnish Papa, and it comes as no great surprise to learn that, "Elton is more of a fun daddy, I think, and I'm the more practical papa." Zachary understands that his father "plays the piano and sings for people", which must seem obvious to him, because John sings to the boys and plays for them all the time. Their favourites are Zip-a-Dee-Doo-Dah, with the lyrics changed to Zacharydoodah, while for Elijah it's Delilah. Furnish couldn't care less if the boys grow up gay or straight. The only thing he is very clear about is that they must not grow up spoilt.

"As they get older, I want them to have jobs around the house, so they have to earn their pocket money, and realise that we do live an extraordinary life, and know that Daddy grew up on a council estate in Pinner, and has worked very hard his whole life to provide all this." Furnish had been expected to pay his own way by his own parents once he turned 18. "There's no such thing as a free ride in my family, and all those things give you a really strong sense of identity and self-worth, and I really want to give it to them."

The couple own five homes – as well as the two in America, they have houses in Windsor, Venice and the south of France, and Furnish laughingly admits, "We're both famously fastidious, both neat freaks, and have a lot of pride in our home and the way things are. Elton is a man who can't go to sleep at night if the remote control for the television is not in perfect alignment with the TV. And with kids, as everyone knows, it just isn't like that. It all just goes out the window. The best comment Elton has said about having children is that, 'Everything I thought I would find annoying, I find absolutely enchanting.' Now there are toys all over the house, and inflatables in the pool, and he just finds that all enchanting." 

Leaving the house poses slightly more of a challenge. Furnish can take the boys anywhere, but has never been able to go out freely with his husband. "The reality is that you don't really go out. If you do, you take security, and it's a military operation: where's the door? Where's the toilet? Where's the seat in the restaurant?" When Furnish wanted to take him to an open-air mall in LA to see how much Zachary loved its Thomas the Tank Engine ride, they decided to give it a go, and took along security. "And actually, the interesting thing was, people were not coming up in the way they do when Elton is on his own. I think they could see it was family time, and I'm really happy about that." 

In September 2015, Zachary starts school in Windsor, so the family are going to settle here. "Last year Elton did 122 shows and over 200 flights, but when Zachary starts school, he's not going to be on the other side of the world when his son's playing football or it's the father-and-son breakfast day." This summer John's appendix ruptured "and he is very, very lucky to be alive. So you start to look at your health. Elton's always been a workhorse, but he wants to look after himself to watch his children grow up."

When the children are older, Furnish hopes to take them to Ukraine to meet Lev and his brother, "So they can understand their journey." By then, he and John will be legally married – "Definitely. People have fought long and hard for equality, and this is all part of that." And he hopes that everyone in Britain will have been tested for HIV.