There’s a perfect Arianna moment during our long interview in the heat of the Los Angeles summer, when I ask her whether she’s seen Swing Vote, a highly topical film that had just opened in America, starring and bankrolled by Kevin Costner. “Yes,” she says. “I am in it…” Pause. “I play myself.”

Well, of course she does. In a film whose central premise is that the outcome of a US presidential election hangs on the vote of one “ordinary American” – that most sought-after coupling of words in this charged real election – the extraordinary Arianna Huffington with her hugely influential political blog (key postings by Barack Obama and Hillary Clinton), The Huffington Post, aka HuffPo, practically commands a cameo role.

There are a number of reasons why I laugh out loud. La Huff’s slightly huffy (forgive the pun but it happens to be true) presumption that, surely, I should already be aware of her small but significant part; her insouciance about the obviousness of her role as a player in Hollywood; the whole slightly nutty reality TV idea of it is funny. It’s just too much, don’t you agree? Probably not, judging by Arianna’s blank response: “I thought that was why you were mentioning it.”

Our day together started chaotically. I arrived bang on time at Huffington’s home, a Mediterranean old-style villa in the swish Bel-Air borders of Brentwood, which once boasted Hollywood royals Gary Cooper, Clark Gable and Joan Crawford as residents, and latterly O.J. Simpson. The photo shoot was supposed to have finished but had not even started, which offered the opportunity for a longish perusal of the property.

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The somewhat madhouse atmosphere, full of keen interns declaring their work is “awesome”, is amplified by a singsong woman’s voice on an endless loop – the Velvet Underground, it turns out, by way of the Juno soundtrack: “I’m sticking with you, ’cos I’m made out of glue, Anything that you might do, I’m gonna do too.”

Beyond the impeccably green collection of Prius cars (or Prii, as Huffington tells me her daughters call them), the front door opens into a vast hallway which would be perfect for the high-powered networking gatherings that were once considered, but no longer, to be Huffington’s central raison d’être. The French windows open out to an extended courtyard with steps leading down to a swimming pool and cabana, flanked by guest houses with wings for the various members of Arianna’s extended family – her late mother, Elli, used to live with her, and her younger sister, Agapi, 56, still does – whom she describes as her “tribe”.

A large dining-room table is covered in platters of fresh fruit and plates of honey-oozing baklava – Arianna has inherited her mother’s hospitality gene – which are intermittently snarfed by the great traffic of people passing through the house. Lempicka lookalikes are on the walls, and a blue portrait by Françoise Gilot; Arianna insists that it was Picasso who copied his ex-wife during his Blue Period, rather than the other way round. There are many, many photographs – almost all of family but also one of Barack Obama who seems, at first glance, to be stroking Arianna’s neck in a gesture of infinite tenderness, while she gazes at him. When I bring this to her attention, Arianna says he was merely gesticulating (which is clearer on close inspection), and then she points out her 19-year-old daughter, Christina, in the background.

Half an hour passes, and Arianna appears, trim in black, only to disappear again, stripping off her shirt to reveal her bra as she jogs up the sweeping staircase. Hair recoiffed, a change of clothes for the last lot of photos, poised on a column of her dozen books, ranging from her early biographies on Picasso and Maria Callas to her recent self-helpish bestseller, On Becoming Fearless, via the political – Right is Wrong, with the longest subtitle: How the lunatic fringe hijacked America, shredded the Constitution, and made us all less safe (and what you need to know to end the madness).

Finally, La Huff has done posing and sits to talk by my side at the giant table. Among the flurry of interruptions and disturbances, there is a sense of contained stillness and calm about her, as well as an unusual quality of simultaneous engagement and detachment. I wonder whether this is a result of so many years of New Age training or because she sometimes doesn’t quite catch the nuance of a question or maybe it’s just a technique for remaining unflappable. I had caught Arianna being grilled by Paxman on Newsnight a week before we met, and his incredulous eyebrow and withering tone didn’t faze her in the least. If anything, she got the better of him.

At 58, she still has the looks of a woman who might flick her burnished mane but she does not. In fact, there is something strikingly unanimated about her. The only tic Arianna seems to have is to knock on the table whenever she says “touch wood”, which is her response to anything from her hope that America is well and truly ready for change to her younger daughter overcoming anorexia.

She is the coolest warm person I have ever met, with a tepid social laugh and a constant refrain that many of her natural inclinations are to do with her “Greek peasant” stock. There are certain contexts where this works: her shrugged-off explanation for the youthful glow of her unstretched skin, and some which make her sound rather less empathic.

When we talk about Isabella’s anorexia, for instance, which she wrote about (with her daughter’s permission) in Fearless, I ask her whether she has ever suffered from anything similar: “No, it’s not a Greek peasant girl disease,” she says. “I always consider myself from Greek peasant stock, I don’t know if I am or not, but I feel I have this earthiness and there’s a sense of perspective that food is precious and I don’t suffer from all these diseases of civilisation.” One takes her point, but I wonder how helpful this robust distaste for modern-day afflictions might have been when her 11-year-old daughter, now 17, was suffering.

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