Many people will know Gregg Wallace as the former greengrocer-turned-MasterChef-co-presenter alongside John Torode – and a man who really, really loves a pudding. Not many people think he can cook, though.

"They don't realise!" says Wallace. "Unfortunately on MasterChef they don't let me cook – I love to cook, but they don't want me to, they want John to be the cook. You can't work with food for 25 odd years and not be interested in cooking."

He admits his cooking skills have evolved however, particularly since he met his fourth wife, Anna, who's Italian. "I do a lot more cooking than I ever did and it's because of Anna and her family [they're from the Lazio region near Rome]. Oh my god, I've learned so much from her!"

So much so that the couple have now written a cookbook together, Gregg's Italian Family Cookbook. But while the MasterChef and Eat Well For Less presenter has laid claim to some of the recipes, really it's all born out of the food Anna, her mum Rina, dad Massimo and Roman nonna, have been making for years. It was merely a "happy accident" that Wallace married into a family where food is the beating heart.

"It was food that got me and Anna close together," the London-born 54-year-old explains."That Italian approach to food is something that I've always, always liked, and to find out that I was falling in love with a girl who was an incredible cook, and then to find out that her family were also incredible cooks, was quite a revelation for me.

"I realised, alongside a beautiful girl, I was joining a family," he adds.

Wallace met Anna, 21 years his junior, back in 2013 (she apparently made contact on Twitter to discuss a rhubarb and duck recipe), three years before they tied the knot. They welcomed their first child into the world, a boy, Sid, earlier this year.

Wallace's love affair with Italian cuisine began when he made a series that saw him travel through the country with the late Charlie Hicks, and first sat down to a simple plate of orecchiette (ear-shapped pasta) in Puglia. "I was just like, 'Wow, food shouldn't taste this good'," he recalls. "From that point on, I've been completely and utterly in love with the food of Italy.

"I love that it's relatively simple, and that it comes out of necessity, most of it, feeding big families on very little – it's just so ridiculously clever."

Big, everyday family feasts, everyone gathered in the kitchen, was a central part of Anna's upbringing, spending school holidays in her nonna's house in Roma, sucking the heads of prawns as a toddler and learning how to cook. "The whole family cooks, and I'm proud of this, they recognise my Anna as the best cook – she used to come home from school and cook dinner for her parents," Wallace says. "She's a far better cook than me."

Their cookbook is a collection of easy-to-make Italian classics –"I don't want to innovate, most are incredibly simple, and that's the point" – and you'll likely recognise nearly all of the dishes. Think pizza bianca, grilled sardines and salsa di pomodoro – recipes that don't require many steps or ingredients. A few you might never have tried, like gnocchi alla romana, made from semolina instead of potato, or ribollita (Tuscan bread soup), and some require a bit more time and effort, like Rina's porchetta (Roman roast pork belly).

Wallace says he's learned a lot from Rina. "I love bagna cauda [a sauce made from anchovies and garlic] but it kept splitting so I phoned my mate Michel Roux Jr. at the Gavroche and he said, 'The oil is too hot'. So I kept trying and it kept splitting. Anna's mum came along and put a spoon of milk in it, and it just emulsified beautifully," he says, laughing. "Michel Roux nil, Reni Sterpini one!

"They've taught me how to make pizza dough – I can't roll it round though, mine still looks like a map of Africa," he adds. "They've taught me how to make fresh pasta in minutes. Anna's taught me better fish cooking, she's taught me better meat cooking, she's taught me everything.

"And her dad? I've never seen anybody cook squid like that on the barbecue, and his rabbit is off the scale. That man just barbecues, he wasn't brought up with a stove."

In Italian homes, it's as much about the act of preparing a meal as it is eating it. "Her family have taught me to just slow down," says Wallace. "It's either you're properly going to sit down and prepare and eat lunch, or you're not going to bother at all. It's not a labour to prepare meals for people."

You may imagine that simple Italian dishes are delicious because the ingredients are better or fresher, but Wallace says that's a common misconception. "In Italy, they don't have fresh tomatoes in winter, they make passata, they use tins of tomatoes.

"What you need to do is start relying on tinned tomatoes, vegetables in oil, tinned tuna; all of these things are good and they're cheap and they're fine. If you've got tins of tomatoes, tins of fish in brine or oil and you've got flour – then you've got hundreds of dishes!"

What about puddings then? Well, that's one thing Wallace still thinks the British do better – although, he adds: "Anna's coffee panna cotta is a thing of absolute beauty."

l Gregg's Italian Family Cookbook by Gregg & Anna Wallace is published by Mitchell Beazley, priced £20.