I am sitting on a plump sofa in the Dorchester hotel facing Enya, whose own sofa is quite rightly even plumper, and I tell her that, having read up on her these past few days, I have come to the conclusion that she is that rarest of things: a genuine enigma. No matter how much one reads about the so-called Queen of New Age music – she sings in English, Latin and Gaelic, and always as if in the midst of a blissful daydream – the woman herself remains steeped in mystery. Presumably, I ask, this is precisely how she likes it?
The smile I had anticipated never quite reaches her lips, and from beneath her raven hair she appraises me quizzically with Bambi eyes.
"I have never tried to create an enigma," she says, gently but firmly. "I have just always been a very independent person."
In the flesh, she is birdlike and elegant in a trim white dress, understated jewellery dripping from her wrists and adorning several fingers. She looks younger than her 54 years, and despite the grandeur of the setting – the Dorchester is a hotel popular among the world's wealthier individuals – she must be the most unlikely music superstar in operation today. But superstar is what she is. In a career now spanning four decades, Enya has very quietly shifted 75 million albums.
"I'm amazed by how my fans have stuck with me," she says, "not least because I am such a slow composer."
Since 1988's breakthrough album, Watermark, which featured the worldwide hit "Orinoco Flow", a gossamer-light slice of musical ambrosia whose ripples have reverberated throughout meditative muzak ever since, she has released just seven albums. Hers is the purest voice this side of angels, but Enya has a distinct advantage over the angels: she exists. Each album has sold remarkably well despite precious little promotion, and a curious refusal to tour. Her 2000 album, A Day Without Rain, for example, which didn't feature in any critic's best-of-year polls, sold 16 million copies around the world. It's been a long time since U2 sold 16 million albums.
"I've been told I have a cross-generational appeal," she says, "and that people who used to like 'Orinoco Flow' are now playing my music to their children. I've been very lucky."
Her new album, Dark Sky Island, is her first in seven years. Like everything she has ever done, it is instantaneously recognisable as the work of the three people that have always toiled to make Enya Enya: producer Nicky Ryan, his lyricist wife Roma, and the woman herself, who writes all the music, sings the songs, and publicly fronts the project. The material they create is music for cathedrals, for yoga sessions. It is aural bubble bath, serene and celestial.
"Oh, but I always feel I am doing something completely different with each new album," she claims, telling me she is a fan of both Green Day and P Diddy, and influenced by both. She points out that several songs here have a stronger beat, and even a little hip-hop influence. I do not spot the hip-hop influence, but she does perhaps express more naked emotion on this record than she has on predecessors. The track "Even in the Shadows", for one, is surely a lament to lost love. "Wonder why this love is over, wonder why it's not forever," she sings.
"Ah," she says. "That song is me exposing myself. It's a heartbreak song. I've never done a heartbreak song before."
One of the things that plays so well into the Enya enigma is that she lives alone, and by all accounts always has done. Home is a large castle just outside Dublin. She has never married, never had children.
"I am single, yes," she says. "But as the song suggests, there have been… relationships. It's quite hard to have someone accept that – well, not that they are second to the music, but that I do need a certain amount of space for it. And even though the person will understand that at the beginning, there is something like jealousy towards the music after a while." She sighs. "It's difficult."
Enya was born Eithne Ní Bhraonáin in Ireland in 1961, one of nine children. At the age of 19, she briefly joined the family band, Clannad, who themselves were enjoying global success with music of a distinctly soporific nature. But she struck out with the Ryans a few years later, and has never looked back. She was a multi-million selling multi-millionaire before her 30th birthday, and they have conjured their enduring musical spell ever since.
There has been a seven-year gap between her last album, 2008's And Winter Came, and Dark Sky Island because she felt that she, and the music, needed it. She bought herself a house in the south of France and did it up, and travelled, visiting family members in Australia. The rest of the time was spent behind her castle walls.
She bought the place in 1997. It sits next to Bono's house, and by all accounts is bigger. It might even be better fortified – and with good reason, for Enya attracts stalkers. There have been several disturbing incidents: a self-harming Italian fan roaming its perimeter; and two separate occasions when fans managed to penetrate the castle's walls. It has been reported that she has had a panic room installed in case of further intrusions.
"It's been traumatic," she says. "I get letters from people saying they are coming to meet me. But, you know, I sympathise with these people because I sense that they are very disturbed. They are leaning towards the music, or to me, for other reasons. They need help."
She cannot say much more on the subject, because the problem is ongoing. She received the latest letter just last week. "The police are investigating."
Perhaps this is partly the reason why she doesn't tour, and keeps public life to a minimum, a recluse seemingly content to make, time and again, music perfect for sun salutations and downward dogs. I ask whether she has ever attended yoga classes herself, and if her songs had ever been used as the soundtrack?
She smiles. "I don't do yoga, but I do do Pilates. Not classes; I have an instructor that comes to me. I do it in the privacy of my own home."
'Dark Sea Island' is released on 20 November