Since she announced the trip late last year, Brightman has been accused of using it as a publicity stunt. But she's used to sniping. It began in 1981, when she caught the married Lloyd Webber's eye in the auditions for Cats, earning her the label of home-breaking, jumped-up gold-digger. When she relaunched herself as a classical singer, many howled at her temerity, disregarding her four-octave range and training at the prestigious Juilliard School. When she vanished to the United States, after she and Lloyd Webber divorced in 1991, they cried "good riddance".
Brightman has had the last laugh. Now 52, she quietly reinvented herself as the world's best-selling soprano, adored everywhere from Korea to Norway, revered for her duet with Andrea Bocelli, Time To Say Goodbye. She's sold more than 30 million records and regularly performs to packed arenas.
In the US, where her albums have outsold Sir Elton John's and the Rolling Stones' for many years, she's known as "the angel of music". She's performed the theme songs at two Olympics (Barcelona and Beijing) and her fortune is estimated at around $55 million.
For years her reputation was that of a touchy diva, but something has mellowed. She's immensely warm and endearing company.
She once had a reputation for callousness. To the question about whether she'd hurt the first Mrs Lloyd Webber, she responded: "I've no idea, you will have to ask her."
Being replaced by the third Mrs Lloyd Webber was described as "not so much upsetting as unsettling". Of her father's suicide, she proclaimed: "He did the right thing". Critics pronounced her heartless. My take is that, as one of life's go-getters, she simply can't be doing with niceties and euphemism.
There's no false modesty there: when I admire her toned upper arms and say she must be very fit, she doesn't demur, but replies blithely: "Yes, I am!"
Talking about her forthcoming adventure, Brightman is full of self-belief. "It's been extremely inspiring and sort of a relief for me as well to be able to do something like this," she says. She'd long booked one of the first $220,000 tickets on Virgin Galactic's planned flights, but with no firm programme yet in place, she was intrigued by the news that for a hefty price the Russians were offering a spare seat on their Soyuz, with the launch date just two years away.
She submitted herself to tests in Houston, passing with flying colours.
The next step was training at Star City in Russia, the space centre on the outskirts of Moscow that has prepared every Russian cosmonaut since Yuri Gagarin. There, Brightman replicated conditions of the space flight, spinning in a centrifuge at 274km/h and withstanding eight times the force of gravity in preparation for take-off, which former astronauts on the craft describe as "like having a bear sitting on your chest". She spent 10 minutes in a rotating chair and underwent a series of psychological tests. "It was full on. I didn't know what to expect but it was far more than I could've expected. But I'd already sort of been trained for it by all my years of touring, in terms of the uncomfortableness, not knowing what to expect, having to create something out of nothing."
There'll be two other astronauts in the craft with Brightman, during the two days it takes to get to the space station. Conditions have been described as like "three men crammed into the front of a Mini with their knees up". She offered to lose weight for the trip, but the Russians told her not to; the Soyuz was built for men, "so if you're a heavier female it's completely fine".
"I'm feeling anticipation about the flight, but no apprehension, just how I feel before I go on stage," she says.
Brightman won't reveal the financial details of the flight, simply saying it's been made possible through her own fortune and sponsorship. The Russians have denied rumours that she "bumped" an American astronaut from the flight by outbidding Nasa. However, the space agency Roscosmos has warned Brightman still may have to step down in favour of a professional spaceman if the flight is extended from eight days to a month.
While she waits for take-off, there's yet another world tour to complete and an album, Dreamchaser, to promote. Influenced by her forthcoming adventure, Dreamchaser is a surprisingly eclectic mix of songs. "It was fun choosing the music, I wanted it to be expansive and have a very positive message and have a lot of energy." Brightman exudes old-hand professionalism, as well as total self-sufficiency, the result of being on stage from the age of 3. At 14, she left home to board at ballet school; she didn't realise the power of her voice until her late teens. "I excelled at ballet and I enjoyed the competitiveness. It made me understand how the world works, it made me knowledgeable about disappointment at an early age."
She relishes her nomadic existence, but the men in her life have found it tricky. Lord Lloyd Webber has confirmed that her refusal to play the society hostess meant curtains for their marriage (the second for both of them).
"It was clear pretty quickly that she was not someone who was going to make a huge home," he once said. "Sarah is a gypsy. She shouldn't marry anyone because she's not the marrying sort. Her world is performing, travelling."
Their parting was acrimonious: Lloyd Webber hinted she had been unfaithful, something she's always denied, and that she was less heartbroken about losing him than about the damage to her career. Brightman retorted by trying to return her $11 million divorce settlement (Lloyd Webber insisted she keep it, saying she'd earned it).
Twenty-three years on, it's all water under the bridge. "My ex-husband's a sweet man and we have a sweet relationship," she says graciously.
She speaks with an upbeat tone when she talks about sad times, which can make her sound cold, but she deals with pain by moving relentlessly forward. In 1992, she was lambasted for appearing in Aspects of Love the night after her businessman father had killed himself by asphyxiation.
"It was something I could grab on to and focus on; my way of getting through those awful, horrific days," she says now. "I felt as if I was in some kind of middle place. If a parent does something like that, all the things you've been brought up with about how precious life is and why we're here go out of the window."
While in an 11-year relationship with German record producer Frank Peterson, Brightman endured two miscarriages, followed by four failed IVF attempts.
She says she doesn't really live anywhere, because she's always travelling, but her main residence is a Cape Cod-style bungalow near the beach in LA. She says she has a boyfriend. "He's American, we've been seeing each other for about a year-and-a-half and it's very lovely, because it's very slow. When you get older you don't want to make any mistakes, you want to be very careful. I don't know what will happen, but I'm very very relaxed about it."
She has the same attitude to going into space. Assuming things go to plan, what will she actually do up there? Will she sing?
"I don't know how possible that is - there are lots of things to look into. But being a singer, I think it would be the right experiment to see what happens if I open my lungs up there."