I’m having breakfast with Mem Fox, whose 2004 children’s book, Where is the Green Sheep? , I have read to my children approximately 2004 times.

I wonder if I should kill her.

”You must’ve gone berserk with it,” says Fox. ”I’m so sorry.”

She tells me an earlier book, Hattie and the Fox, was so popular with her hairdresser’s son that her hairdresser told her, ”I’m going to not cut your hair today, Mem, I’m going to cut your throat.”

Fox, 67, decided to be a writer when she was 22 but didn’t publish her first book until she was 37. That book, Possum Magic, written as an exercise in a university class, was the Green Sheep of its generation. It has sold more than 3 million copies, and Fox is candid about the secret of its success.

”As you well know,” she says, ”you pick up a picture book to read with a child, and you look at the amount of text and go ‘Oh no, not that one. Let’s put that one quickly back on the shelf.’ I honestly believe – and this is serious, I’m not sending myself up – that one of the reasons for my continuing great popularity among parents is because my books are short. They think, ‘Oh, Mem Fox, that’ll be great. It’ll only take two minutes.’ And the latest, which is for babies, takes one minute 10 seconds.”

We’re having breakfast at the Promenade Restaurant of the Stamford Grand Adelaide Hotel in beachside Glenelg. Fox lives in nearby Brighton, but I had to get up at 5am to arrive here for 9am, so the meal feels more like my lunch. As Fox picks at a rather small bowl of fruit and half a croissant, I demolish three hash browns and three sausages.

The slightly shabby Grand has a deceptively stately feel, at least at breakfast time. Piped piano music plays in the dining room. Disconcertingly, it seems to well up when Fox becomes emotive, as if it were somehow a soundtrack that followed her around. Although Fox booked a table for us, because she feared it might be crowded, there’s virtually nobody here. But then, Fox doesn’t really know much about what goes on before the shops open.

”I’m not an early-morning person,” she says. ”Breakfasts have always confused me as a concept.”

Fox is trim and bubbly, slightly elfin, with short hair and what she says are sticky-out ears. She laughs easily and talks freely. ”I’m a rabbitter on,” she says. ”I love rabbiting on.”

She hoped it would be a beautiful day for me in Glenelg, but the heatwave has broken and a storm darkens the skies over Holdfast Bay. There’s a view to the ocean from the tall windows of the Promenade Restaurant, and the only human being on the horizon is an elderly man motoring to the end of the pier on his mobility scooter, his red safety flag flapping wildly in the gathering wind. The scene looks like a Jeffrey Smart painting, a commentary on loneliness.

”At least he won’t get blown off,” says Fox. ”He’s on a heavy vehicle there.”

Fox had to get up this morning to take her three-year-old grandson, Theo, to kindy. Fox’s daughter, the South Australian Labor politician Chloe Fox, is a single mother, and Fox and her husband, Malcolm, are heavily involved in looking after the little boy.

”He’s more like a son,” says Fox, ”and we don’t mind. I mean, we’re both exhausted because we’re in our late 60s, but he’s the only grandson we’ll have and he’ll be at school in a year. What’s more important than interacting with that child? For us, nothing.”

There is one other thing. She has a ”gravely ill” sister in hospital in NSW, and she’s going up to visit her the next day.

”My sister’s illness and caring for my grandson outweigh anything else in my life,” she says. ”If I never wrote again, I wouldn’t care.”

Fox migrated to Australia in 1970 as a £10 Pom, which was odd, since she was born in Melbourne in 1946. From the age of six months, she grew up in what was then Southern Rhodesia (now Zimbabwe), where her parents worked as education missionaries for the London Missionary Society. She was educated at an all-white girls’ school in Bulawayo, then moved to London to attend drama school in 1965.

Her religious upbringing seems to have left her little comfort.

”I have a friend with cancer at the moment,” she says. ”I wrote to her last night and said, ‘You are constantly in my thoughts but never in my prayers, because they don’t work, and I’ve lived long enough for that to be proved over and over and over again. So I will not be praying for you. Ever.’ ”

Mem met Malcolm, a teacher, in London, and in 1969 they moved to Rwanda, where they worked at a university. ”I can’t believe it,” she says, ”sitting here in Glenelg, being who I am now, and looking back at that 22-year-old in the middle of nowhere, teaching people who loathed each other, the Hutus and the Tutsis in the same class.”

She and Malcolm were barely older than their students. After six months in Rwanda, they migrated to Australia. She remembers a warm and welcoming immigration officer, with whom she was obliged to share her real name.

”My full name I cannot reveal to you,” she says, ”because it’s so awful.”

Tell me. I want to put it in the paper.

”I’m sure it’s findable on the website,” she says. ”It’s the name of Parliament Square in Dublin, and we have no Irish connection whatsoever. It’s also the name of a posh hotel in that same square. So I decided that when I’m 70 I’m going to find my best friend from high school and she and I are going to go for a girls’ weekend to the Hotel M- in M-Square, Dublin, for our 70th birthday.”

I experimentally address her as ”Mesopotamia”.

”Close,” she says.

Fortified by a belly full of hash browns and sausages, I find the courage to ask Fox the question on the lips of every investigative journalist: is the green sheep based on an actual sheep?

”No,” says Fox, ”it’s not.”

She laughs.

”Western Victoria’s going to have a sheepathon or something like that next year,” she says, ”a big sheep festival in Hamilton – and I think they’re going to hide copies of the Green Sheep all over the town, and they’ve taken a photo of two massive woolly sheep reading the Green Sheep.”

How can she tell the sheep are reading? It sounds like they’re grazing.

At this point, it might be worth recapping the story of Fox’s ovine classic. There are a number of sheep, each with a particular defining characteristic, none of which are generally associated with sheep. They may, for instance, be blue or red, in the bath or in the bed. They are introduced in rhyming couplets and, at the end of every verse, the immortal query sounds: ”But where is the green sheep?”

And that’s it. Children like looking for the Green Sheep, even though they know exactly where it is and they found it yesterday, the day before, and every other day for as far back as they can remember.

And now, in the supermarket, when people stop Fox and tell her, in that strange way people do, the one thing she is certain to know already – ”You’re Mem Fox” – and add ”I just love your book”, she knows , ”among the 40 I’ve written”, they are talking about The Green Sheep.

Fox spent most of her career as an academic, and was an associate professor in literary studies at Flinders University when she resigned, aged 50, in surrender to the ”peripheral, maddening banalities associated with the business of being a writer”. She says she loved teaching, and she was ”very strict, but loved” by her students. Her classes, on her insistence, were three hours’ long, and her course was compulsory, ”but they were lovely,” she says, ”and they said three hours with me passed like … ”

Six days?

She laughs. ”Six days with other people, yes.”

”Maddening banalities” such as marketing still plague her life. She has just finished touring to promote her 40th book, Baby Bedtime.

”To the audience, it’s just another Mem Fox book,” she says, ”but it isn’t … ”

Because she didn’t write it?

By this time, she has learnt to ignore me.

Her grandson, she says, was born two months premature and weighing only a kilo.

”Despite the fact he wasn’t beautiful to look at,” she says, ”it seemed to me he was the most beautiful thing that had ever lived. And I said to him, in one breath, almost, ‘I could eat your little ears, I could nibble on your nose, I could munch your tiny fingers, I could gobble up your toes.’ That’s the first verse of my book.”

She refuses to tell me her real name, even when the interview is over, but she’s right – it’s on the internet. Disappointingly, it’s not ridiculous, but I won’t spoil the secret. On the other hand, if you really need know where the Green Sheep is, I can reveal it’s behind a bush, ”fast asleep”.

There. Now you don’t have to read it. Again.

MARK DAPIN  |  THE SYDNEY MORNING HERALD, 4 JANUARY 2014