There’s a certain ironic sting that in order to be her own person again, Kay Hartenstein felt the need to re-adopt the surname of her ex-husband, the art collector and spouse of Nigella Lawson, Charles Saatchi. For a while, in the difficult aftermath of that very public decoupling, the American art dealer turned collector and now curator reverted to her maiden name: “But really no one knows me as Kay Hartenstein here; nobody knows that I did that gallery with Charles all those years. It would be like starting out all over again. Even in LA, I’m known as Kay Saatchi in the art world, which means I have something to bring to the dinner table,” she says. “Charles would rather I had gone back to my maiden name but it’s part of me – and part of something I did for a long, long time, and it’s very good for getting tables at the Wolseley.”

It’s only in the last three years, since the couple’s divorce in 2001, that Kay has come out of the shadows and had the confidence to return to the art world, which had been her world, too, before she joined forces with Charles. For the first four years, she was “licking her wounds and lying very low”, dealing with multiple losses; apart from the end of a marriage which had been in trouble but which she had thought was salvageable, her mother and her brother died, as well as both Charles’s parents to whom she had remained close, and the 75-year-old nanny who had looked after the couple’s young daughter, Phoebe, also died of cancer. There had been the loss of her Chelsea home, which she was responsible for selling as part of the divorce settlement, and all the adjustments that diminution entailed: “It was a really hard time – physically and emotionally very draining, compounded by a lot of other loss in my life and a lot of disruption, and I was trying to take care of this little girl who was living in a tiny rented flat which she was unhappy about.”

Meanwhile Nigella, of course, had her own bereavement to deal with – living with and watching the decline of her husband, the journalist John Diamond, who died of cancer. But while only the most mean-spirited would begrudge her the chance to find happiness again, anyone can see that it must have been tough on the supplanted wife to be endlessly confronted with images of such a glamorous successor – in La Lawson’s dramatic trajectory as a domestic, then transatlantic goddess – splashed over billboards from the UK to the USA.

Our first meeting for this piece was in Selfridges’ “art gallery” Ultralounge, at Anticipation – an exhibition of work by some of the most outstanding London art school graduates, co-curated by Kay Saatchi and Catriona Warren. This is a most exciting venture, where a shortlist of 21 blossoming artists show their work and receive 100 per cent of the proceeds of their sales. The public benefits from the collective eye of two aficionados who have done all the hard work visiting the major London art colleges and liaising with the tutors to find young artists who combine talent with the commitment and creative heft to produce distinctive work for the long haul.

Saatchi had already seen the Conrad Shawcross sculptures in that space, as well as Sam Taylor-Wood’s banners elsewhere in Selfridges and various other shows, such as the one on surrealism and urban art. Nonetheless, she admits to having some initial concerns about whether a department store, however stylish, was an appropriate context for the students’ work.

“But people know how hard it is to put on these shows – even the Tate sometimes has problems getting sponsors – and it all depends on how serious the show is when it gets hung,” Kay says. “I said that we needed to run it more like a museum than a commercial art gallery so you can look at the paintings and read what’s written about them on the wall. The artists also need to be there to talk to people and get them to engage because these kids aren’t used to talking about their art that much.

“It’s also to teach people about contemporary art and let them know that buying art doesn’t have to be intimidating. If you’ve ever walked into somewhere like the Gagosian Gallery, it felt like if you asked the price of something they’d laugh at you.”

I happen to be a fan of the first wave of YBAs and, while writing a profile of Damien Hirst, years ago, visited the home Kay then shared with Charles in Chelsea to see Away from the Flock, Hirst’s sheep in a tank of formaldehyde, which had pride of place in the reception. (Kay was amusing on the subject of the importance of hanging works in a way that you can live with them. She found it challenging, for instance, to eat her breakfast gazing at the crotch of one of Jenny Saville’s monumental women – and had the nude moved to somewhere that was not so, quite literally, in her face.)

This Anticipation show, following the success of last year’s, is less about the shock of the new and more about a mining and refining of traditional ideas – there’s an emphasis on painting for instance, and photographs that recall the Grand Masters – married to what could be described as a sort of mind-screw.

Kay is rather maternal in the way that she champions her artists, coaxing the more reserved ones to speak out but with the tact of a diplomat rather than the thrust of a pushy parent, as she click-clacks around the show in her high heels. There’s an amusing moment when we hover in front of Philip Caramazza’s jewel-like work and she says, “Saatchi has expressed interest” – which is striking for all sorts of reasons. She then adds that Charles “and Nigella” have been to the show, which suggests a level of equanimity as well as support from Saatchi but also, perhaps, an appreciation of what his ex-wife and Warren have pulled off.

We next meet in Kay’s home which has a gracious, double-fronted exterior and a tangle of vines, jasmine and clematis leading down to the basement, which is what she has for a garden these days. Inside, everything looks a little over-size – apart from the owner, who is petite – as though the paintings and vases and sculptures started life in a much larger space, which is, of course, the case.

In the living room, where we sit perched at the end of a table dominated by a huge vase of blue delphiniums, one wall is filled with an impressive Paula Rego, which I think I recognise from the Chelsea home. Half the room is occupied by a grand piano which gleams in the semi-darkness; astride it is a massive naked baby by Ron Mueck, the Australian sculptor and Rego’s son-in-law. There’s a collection of Picasso ceramics and a table covered in ancient Egyptian translucent bowls, as well as pieces by lesser known artists which have caught Kay’s eye.

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