Beyoncé, Robbie Williams, The Police, Bob Marley, Aretha Franklin, Enya.

What do all these artists have in common? Apart from the fact they’d have made a heck of a supergroup, they’ve all shifted somewhere in the region of 75 million records (give or take the odd platinum disc). But only one of them has done it in quite such a singular fashion: no tours, no Twitter, no premieres or parties or soft drink sponsorship deals.

There’s a word for this: Enyanomics. Coined by a US businessman, it describes the phenomenon of continued commercial growth in inverse proportion to public exposure. But if you think Eithne Ní Bhraonáin – or Enya Brennan, to use the Anglicised version – sits at home dreaming up ways to game the system, the truth is a lot more prosaic.

‘I’m a very slow writer,’ Enya tells Weekend. Immaculately poised on a sofa at The Dorchester, the 54-year-old has returned to the fray – or as close to the fray as things get in Enya’s world – to promote Dark Sky Island, her first album in seven years. ‘It’s important to have time to work on the songs, then set it aside and come back to it. There’s a lot of trial and error. It’s quite demanding on me. Someone asked me if I have a vast library of songs and I said no – what you hear is all I’ve got!’

There was a time when Enya grew weary of the image of her as an enigmatic recluse, a musical Miss Havisham hiding away in the tower of her Irish castle. But she says she doesn’t worry about it any more.

‘I used to be very resistant to criticism that I didn’t share everything with everyone. I just valued my time and I thought, I give enough, I give the music, and I need time to myself, because I feel the music will suffer if every aspect of my life is read about. I kept saying, “Why are you so fascinated by what I do in my spare time?” But over the years, you do mellow out.’

As for ‘Enyanomics’: ‘It’s not intentional. That’s not how we approach things. I’m a very strong, independent person, always have been, and when anything’s put forward to me, I think about it, and if it’s the right step to take, I take that step.’ Which is to say: if it isn’t, she doesn’t.

Enya is, to all intents and purposes, a trio – ‘a strong example of the power of three, omne trium perfectum’ – as the press biog states, with suitable mysticism. Producer Nicky Ryan is the visionary who lured Enya away from the family business, Irish folk stalwarts Clannad, with the idea of multi-tracking her voice (on some songs, up to 500 times) to create an ethereal ‘virtual choir’. Ryan’s wife Roma is the lyricist, charged with putting Enya’s music (which she writes and performs virtually single-handed) into words. It’s a formula that found an instant worldwide audience on 1988’s Watermark, with its signature hit Orinoco Flow, then just kept on growing, making Enya Ireland’s best-selling ‘solo’ artist of all time, and its second-biggest musical export, after U2.

Dark Sky Island (named in honour of Sark, which the inhabitants have designated a ‘dark sky area’ in order to better appreciate the constellations) doesn’t stray too far from this successful blueprint. With a loose theme of ‘journeys’, it is full of the sort of spiritual, elemental imagery – rain, seas, stars, moons, time – that has allowed Enya’s music to cross all cultural and language barriers. (Some songs are even sung in Ryan’s invented Loxian language, while their contribution to Peter Jackson’s Lord of the Rings soundtrack was in authentic Elvish.)

Having pursued such a distinctive musical style over the decades, does she ever feel like wigging out and giving us, say, Enya’s thrash metal album?

‘If I wanted to, I would,’ she smiles. ‘But it has to feel like a natural progression. That would feel like being pressured to be someone else, and I would ask you: why would I want to be someone else?’

It’s a fair point: being Enya seems to be working out pretty well for her. The sixth of nine children from Gweedore, Country Donegal, young Eithne began performing with her family – as every Irish child appears contractually obliged to do – at the age of 3. ‘Music is a strong part of the Irish culture,’ she explains. ‘Even now, though teenagers are listening to their own music and doing their selfies or whatever, you’ll still see them sitting with their grandparents, learning the fiddle or the concertina.’

She briefly joined her siblings in Clannad, but left with Nicky – then their manager and producer – when the rest of the band resisted his attempts to update their sound with synthesisers and other perceived crimes against musical authenticity. It was acrimonious, but Enya insists any bad blood is ‘absolutely’ in the past: ‘Family is family, and we see each other,’ she says.

For a while, she lived with Nicky and Roma, but is dismissive of Freudian analysis casting them as a surrogate family for the estranged real thing. These days, they live in separate, nearby castles, Enya having bought her crenelated Victorian pile near Dublin in 1997.

She has had high-profile problems with stalkers over the years, including one who got into the castle and tied up a maid, and another who stabbed himself outside her parents’ pub. She describes the situation as ‘ongoing’. ‘When it happens, I have to notify the police. I know immediately, from reading letters, “this is a very disturbed person”. I’m more concerned about them getting care. It’s not something I’m traumatised by any more. At the beginning, yes, but not now.’

Does it come with the territory, or has she been particularly unlucky? ‘Well my gates are very well photographed,’ she says.

Would she ever be tempted to move? ‘Absolutely not. The break-in that happened, they never got into my main home, it was an outhouse, so I feel very safe. And I know how to deal with it now. There are a lot of things to worry about, and that’s not one.’

Weekend asks if it’s fun being Enya. ‘I love it,’ she says, before expounding further on the rewards, frustrations and technical craft of songwriting.

But 75 million record sales, four Grammys, an Ivor Novello, an Oscar nomination, travelling the world, performing for the Pope: it’s been quite a ride. Does she ever just sit back, take a moment and wonder where it all went right?

She considers the question, then says: ‘It doesn’t make it any easier writing songs.’

Dark Sky Island is out now on Warner Bros

Published in Waitrose Weekend, December 3, 2015

(c) Waitrose Weekend