And from there, she flies to Dubai to see the woman on whose childhood her book is based - Princess Haya bint Al Hussein of Jordan.
Her Royal Highness - a mother of two, Olympian, humanitarian, equestrian leader, Messenger of Peace and truck driver - already had her copy of the book.
But Gregg had a one-off leather-bound copy made for her.
"I'm fine with one from the shop," Gregg says, brandishing her bright pink and silver hardback book.
Their choice of book covers notwithstanding, these two women from opposite sides of the world have come to discover they share much in common. Both lost their mothers - strong, influential figures in their lives - at a young age. Both were sent away to boarding schools. And both had their hearts healed by horses.
Before the book's launch in Birmingham, at the "The World's Most Famous Horse Show", Gregg swotted up, re-reading her 17 other pony books. She was afraid of disappointing her fans - predominantly pony-mad tween girls, who memorise characters and narratives; just as Gregg once did as a pony-mad girl with Walter Farley's famed Black Stallion stories.
As she read, the 45-year-old was reduced to tears.
"It's quite funny for an ex-journalist - you would think that I would be so hard, but I'm not," she laughs. "Writing the books, you become so invested in them, and I'm such a wuss.
"When I do readings at schools it's really hard trying to strike that balance between emoting and not bursting into tears halfway through my own book, which is not really a good look. It nearly happened to me at Remuera Primary the other day."
It happened to her when she wrote the first series of Pony Club Secrets in her local cafe, the Garnet Road Foodstore. She went there for the noise: "People would come in and out, banging and crashing, and it was just like a newsroom," she says. "I'd be writing about how Victory had broken his leg on the cross-country course and would have to be put down, and I'd be sobbing over my laptop, then look up and see half the restaurant staring at me. I can't stress enough how emotionally attached I get to the stories."
But none more so than The Princess And The Foal. A departure from Gregg's earlier pony tales, this one is based on the true story of Princess Haya, who at the age of 2 lost her mother, Queen Alia, in a helicopter crash but found solace and strength in raising an orphaned foal given to her by her father, King Hussein on her 6th birthday.
Defying convention, the determined 12-year-old Haya rode the horse, Bint Al Reeh (Daughter of the Wind), in the King's Cup, the toughest equestrian competition in Jordan - the first girl ever to compete. She won.
For years, Gregg collected newspaper clippings and searched for a way to include the princess character in one of her four Pony Club Rivals books, but she was "too big" for the stories. Gregg's publishers, HarperCollins UK, wanted her to branch out into literary fiction and agreed Haya's real-life fairy tale stood out on its own.
Gregg was "an emotional wreck" writing the story, this time in the privacy of her garden shed in Westmere. "I just sat there for weeks on the first chapter, regularly having a good sob. It's hard enough writing fictional characters, but when I thought 'this is really Princess Haya, and I'm trying to put myself into knowing how she felt losing her mum'.
She was such an incredible, gutsy, strident little thing, you know?" she says.
Gregg employed a typically Kiwi approach to get Her Royal Highness on board with the idea of reliving her childhood: she wrote her a letter.
"To be honest, only a New Zealander would have contemplated it. It's the way we think, 'I'll just drop her a line, see what she thinks'," Gregg says. "I got a phone call from her head of affairs, who said 'Why don't you just pop over to Dubai and have a meeting with us?' And it was literally like that - I popped over for a meeting and came home again."
The Princess, charmed by the former magazine editor, gave her blessing for the book.
"I think she very much needed convincing to have her story told; but luckily I'm used to convincing people."
The more she learned about Princess Haya - in person and on the phone, and through visiting staff and family at her old home in Jordan - the more Gregg discovered how their early lives ran parallel.
Their upbringings, were of course, wildly different. Gregg is a commoner, the daughter of a geologist, and grew up in Ngaruawahia, the home of Maori Kingitanga, in the Waikato.
Princess Haya is the daughter of the late King Hussein, revered leader of Jordan for almost 50 years, and grew up in the Royal Palaces in Amman.
Today, the princess moves between residences in England and Dubai, the "junior wife" of one of the most powerful men in the Middle East - His Highness Sheikh Mohammed Bin Rashid Al Maktoum, Vice-President and Prime Minister of the United Arab Emirates.
The Ruler of Dubai is 64; Princess Haya 39. They became friends in 2002, both competing at the World Equestrian Games in Spain, and now have a daughter Al-Jalila, about to turn 6, and a son Zayed, almost 2.
But Princess Haya is a roll-up-your-sleeves kind of leader in her own right. The girl who mucked out horse stables and at 13 became the first female equestrian to represent Jordan, is now the president of the world equestrian body, the FEI. Coming to the end of an unprecedented two terms, she has led the way in globalising and cleaning up horse sport. And the woman who carried the Jordanian flag at the opening ceremony of the 2000 Sydney Olympics, and competed in showjumping (finishing 70th), is now a member of the International Olympic Committee.
With an honours degree in politics, philosophy and economics from Oxford, Princess Haya now cares for Jordan's needy and hungry, running the first food-relief NGO in the Arab world. She set it up in honour of her mother, who aimed to take care of her country's underprivileged before dying tragically in a storm in 1977. She is also a United Nations Messenger of Peace, alongside George Clooney, Stevie Wonder and cellist Yo-Yo Ma.
"I think her achievements will be huge in the next decade, as a force for peace in the Middle East, and for women's rights," Gregg says.
Jordan's first professional athlete, Princess Haya is still the only woman licensed to drive heavy trucks in Jordan. King Hussein called her "the Trucker", and she would regale him with stories she picked up at trucker cafes while driving her horses to competitions.
She is small, regally beautiful, but, in her own words, tough.
"I have such a girl crush on her," Gregg says. "She has this infectious sense of mischief and enthusiasm for life. She doesn't want to be a princess in glass slippers and a gown; she's a tomboy who wants to muck out stables, ride horses and be with her family.
"The things she could do with a horse put her into a superhero category for me. She can do a handstand on a galloping horse! From a very early age she had a single-minded sense of destiny."
Sent to boarding school in England, the only saving grace for Princess Haya was horses, riding with young heiress Jemima Goldsmith who later married Pakistani cricketer Imran Khan.
"Haya was miserable at boarding school," Gregg says. "She told me she always felt short, dark and frumpy next to the gorgeous blond Jemima. She is very self-effacing."
Gregg, on the other hand, loved being a boarder. She was sent from Ngaruawahia High to King's College in Auckland after her mother, Glenda, died during an angiogram. Glenda had gone into Waikato Hospital, suffering pains in her arm, but died from an allergic reaction during the x-ray test. She was 42; Gregg 15.
"It was very sudden and unexpected," Gregg says. "Haya and I share the same sense of being forever in the shadow of someone you think is great. I was extremely close to my mum. Although she didn't love horses, she was good with them; she could plait a mean tail."
It had been Glenda who suggested moving the family from Titirangi to her home town of Ngaruawahia so Gregg and her younger sister - artist and personal trainer Kirsty Gregg - could have ponies. "We wore our parents down," says Gregg, whose passion began as a 5-year-old, when in lieu of a horse, she taught Jones, the family doberman, to jump fences.
Gregg admits most of her writing has been influenced by her mother's death: "So this book was probably a more open, overt acknowledgement of that."
When she produced her first draft of The Princess And The Foal, her London-based editors "felt it was a bit cold", she says. "Then I realised I actually couldn't quite face how emotional I was about it.
"I said to them 'I just don't want to upset the kids who read it'. And they said I had to tell the story like it happened, even though the moment when her mother dies is just awful. There is no greater loss for a child than losing their mum."
"Everything good that has ever happened to me in my life has been because of horses,"
Princess Haya wrote in American kids' horse magazine, Blaze, "from rearing my orphaned foal, to being given the chance to compete by my dad, to being elected president of the FEI and having the honour of being a member of the International Olympic Committee.
Horses even led me to my husband.
"Growing up I always felt truly happy and at peace in the company of horses and they will always give me comfort if ever I need cheering up. I know I am not alone in feeling this way."
On a week-long visit to Jordan's Royal Palaces, Gregg talked to household staff and stablehands who were there when Princess Haya was growing up.
"They all remember her fondly from the days when she used to hang out in the stables and get underfoot. I spoke to the head of household who had rescued Haya's little brother, Ali, from the dumbwaiter after she stuffed him in it," Gregg says.
"She was just a handful. They remember her shaving the King's priceless bearskin rug so she could practise her handstands. But they all adore her."
While Haya's story of training Bint Al Reeh to win the King's Cup for her father's royal team is the basis of The Princess And The Foal, Gregg filled the gaps as she imagined things might have happened.
"It's what Emily Perkins calls 'faction' - a novel based on fact. It was the hardest book I've ever written, but having spent 17 books coming up with the twists and turns and minutiae of plot, it was nice to know where you were going for once," she says. "When I heard from Haya's team after they had read the manuscript that I had captured her - that it felt real to them - I was walking on air.
"While I was writing it, I inhabited her. But Haya is not me; she's much better at being a person. Her ideals are far loftier than mine. But I loved being a better person for that time I was working on it."
Gregg's ability to understand the connection between girl and horse has seen her corner the pony fiction genre in Britain and New Zealand. In Britain alone, the two Pony Club series have sold almost 650,000 copies; the books also sell strongly in France, Spain, Denmark and Belgium. And now she has her first book printed in Arabic.
Nancy Miles, Gregg's literary agent of the Miles Stott Literary Agency, says her Kiwi writer is a joy to work with - never missing a deadline, and taking critique and direction in her long stride.
"When I started working with Stacy she was delivering over two novels a year, each over 50,000 words. She did this for 17 novels which was a punishing schedule by any measure, but if she was feeling the pressure, she didn't show it," Miles says.
"Stacy can remember what the world looks like through a child's eyes. She understands the unique bond girls have with their horses and she brings an emotional depth to her novels which I think makes them distinct from the competition."
Her latest book has the hallmarks, Miles says, of becoming a classic in children's fiction. "This is not just a book for horse lovers, because it has human drama at its heart," she says.
As she rode her pony, Bonnie, around a paddock in the Waikato as a teenager, Gregg dreamed of winning eventing's Grand Slam - Badminton, Burghley and Kentucky. But reality struck hard "when my horse kept refusing in the show ring.
"I just wasn't brave enough. But the great thing about writing the Secrets series, Issie wins the Grand Slam in the final book. So I could vicariously win Badminton! Writing these books is absolutely wish-fulfilment on my part."
Writing children's books is her future now. She misses fashion journalism after two decades as a feature writer, and would still be doing it "if the books hadn't come along".
Her biggest regret is that she and her partner, Michael Lamb, sold the groundbreaking fashion website Runway Reporter, which they started when Gregg was editor of Fashion Quarterly.
"It hurts me hugely that no one has it now, that ACP shuttered it [closed it down] after they bought it. We thought selling a website to a multinational publisher was a no-brainer in terms of keeping it going. It turned out that the sort of 'mom and pop' ingenuity of the way we were doing it was far more viable."
Would she ever return to the glossy world of fashion mags? "I think I am utterly unemployable now. Having worked on magazines for so many years, I just don't think I have the wherewithal to have the conversations anymore. So, luckily, the books worked out."
Gregg is still riding. Most days she drives out west to ride a friend's gentle clydesdale cross called Diesel (she needs a stepladder to climb aboard the 17-hand giant), or watch 13-year-old Isadora on her new pony, Maddie. She's thrilled that her daughter shares her pony passion.
The single-minded little girl who taught her dog to showjump continues to live her horsey dreams, even at 45. She has no intention of growing up.
"People ask when I will write a 'real' novel. I don't know that I ever will," she says. "I think my mental age will always be 12."
