But this is no ordinary pig. "Sit!" she calls sternly and he obliges, planting his considerable bulk into the dust. "Good boy," she gushes as he gently nibbles some feed from her hand.
Thomas - full title Willowbank Te Whangi - is a Kune Kune, a rare breed from New Zealand. Describing the breed on the telephone before my visit, Zoe summed it up thus: "If Disney made a pig, it would be pretty much like this."
The Kune Kune - meaning "fat and round" - lives up to its name, although it is still far smaller than some of the traditional British breeds such as the Gloucester Old Spot. It grows to between 180lb and 220lb and has peculiar goat-like tassles dangling from its cheeks. Piglets are born with hair that grows long and wavy.
But it's more the animal's character that has Zoe and a handful of other breeders completely besotted. Right from birth, the Kune Kune behaves more like man's best friend than a pig.
Zoe opens a stable door and a group of piglets trot out, milling around us like excited puppies. Two of them chew my shoelaces while their mother, Goldie, lies in a corner, seemingly unconcerned that we're touching her offspring.
"This is what's wonderful about the breed," says Zoe enthusiastically. "From the minute they're born they just love people. Traditionally they were kept by the Maoris, who didn't fence them, so the Kunes just hung around the village.
"They're very like dogs, their whole nature. They're great friends and incredibly clever. All my adults will sit on command, and two of them will walk to heel.
"When they're first born and they get to about five days old, they fight like mad with one another for dominance because the teats near the front have more milk. For the first few days they get torn ears and they lose tassles. They're vicious, horrible things - then they grow out of it, and that's it."
Zoe, a 35-year-old vet's assistant, also teaches horse riding and has occasionally supplied animals for TV. One of her cockerels recently appeared in Brookside. On her parents' smallholding near Chester she keeps an Andalucian stallion, a llama, two ferrets and a couple of chinchillas. But she never dreamed she'd end up rearing pigs.
Then, a few years back, she and partner Andrew Calveley, a horticulturist, were working in New Zealand when they first saw a Kune Kune at a Christchurch wildlife reserve. They were smitten.
The breed was thought to have originated in China, but nobody knew for sure whether Maoris or western settlers first introduced it to New Zealand.
For centuries it was kept by the Maoris for meat, but by the late 1970s there were only 50 or so left. Conservationists Michael Willis and John Simister set out to save it, buying every Kune they could find. Today, thanks to their efforts, there are more than 1,000 registered in New Zealand, and the number is growing.
Zoe decided to do her bit to safeguard the breed and braved a bureaucratic maze to introduce it into Britain. In 1992 she imported five pure-bred pedigree pigs - three sows and two boars. The following year, as interest grew, she brought six more pigs over and helped found the British Kune Kune Society.
Today she has 35. From the original imports, she has sold breeding pairs to people in Dorset, Staffordshire, Coventry and the Isle of Mull, and many more individual pigs.
They don't smell, she says, and even the adults eat relatively little. "These are grazing pigs. They eat mainly grass, vegetables, fruit. Rebecca here is raising her piglets on about 8lb of grain a day, which is absolutely nothing compared with a normal pig. They live on fresh air."
And here lies the dilemma. The Kune Kune, good-natured, intelligent, clean and above all cute, does make an excellent pet as long as you have the room. But that could also become its downfall, especially if it were to go the same way as the Vietnamese Pot Bellied Pig.
Heather Powles from County Durham, who runs the Pot Bellied Pig Club, says: "They became the yuppie pet of the late 1980s, fetching quite high prices. I think a lot of people jumped on the bandwagon, thinking they were going to make a fortune breeding and selling them. But it didn't happen and the price dropped to rock-bottom.
"Now they have been abandoned all over the country. I even had somebody on the phone to me last night from Birmingham, telling me about an advert in a paper offering one free to the first taker. It said: `Will make excellent curry.'
"People would go out, see a wee piglet - and they do look absolutely adorable - and they'd buy it not knowing the first thing about it. But when it starts to grow, and when it wrecks the garden and the house, they get rid of it."
The legacy, says Heather, is a cruel one. "I've seen so many of these poor pigs overweight. It's so cruel and leads to all sorts of problems - they become lame, prone to pneumonia, and they go blind because there's so much fat around the eyes. Often people don't even realise what a healthy one should look like."
Zoe Lindop is adamant the Kune Kune will not go the same way. "Yes, Kunes are excellent pets but only if you've got room. If somebody rings up and says, `I've got a garden', I say, `Ever so sorry, but no. Come and see the pigs here by all means, but if you buy one you won't be happy, the pig won't be happy. You really need at least half an acre.' "
She believes it's down to breeders like herself to be responsible, and agrees with the Rare Breeds Survival Trust's approach. The trust recently announced that it will encourage people to eat rare farm animals to create a good commercial niche and thereby ensure that they survive.
"The Kune Kune needs promoting in terms of what it's good at," says Zoe. "Which is being a very, very pleasant creature to have about, but which will at the same time raise meat for you. They are good meat pigs - I don't want them thought of just as pets. Back in New Zealand they're really popular. It's because there a lot of people have 10 or 20 acres and raise their own meat.
"These pigs are brilliant for that because you keep your sow as a member of the family, but you eat the piglets. They are kept for meat and they are very good meat.
"Apparently, until they're about a year old it's very nicely marbled with fat so it cooks very well and there's a really good flavour to it. I know people who've had it say that this is how pork used to taste."
She's never tried any herself, though. Rearing Kunes is an expensive business, and as she sells breeding adults for upwards of pounds 500 each, and still makes little profit, she's not likely to squander one on Sunday lunch.
Also, she's hand-reared some of hers, even allowing them into the house. The bottom line is, they're just too darned friendly.
"I don't know if I could eat one of my own," she admits, staring lovingly at a group of piglets. "But I would eat someone else's. I really do think they should be eaten, because what use is a pig if you can't eat it?"Reuse content