Getting to speak to Paul Hollywood and Mary Berry is not easy. If you imagine trying to persuade the pope to pose for photographs alongside Madonna, Barack Obama and all five members of One Direction, you get some small idea of the hype surrounding these two unexpected stars of the small screen.

The Great British Bake Off was the hit of the year – a soufflé of niceness in the midst of schedules dominated by talent show nastiness – and Paul and Mary, the show's judges, have been catapulted into the celebrity firmament. Their diaries are filled months in advance with TV appearances, radio interviews and cooking demonstrations. I grab an hour with them in the green room at Radio 2, just after they've appeared on the Chris Evans breakfast show and just before they are bundled into a car with blacked-out windows to be driven to Loose Women. Is it strange, I wonder, suddenly being this famous?

"I think the nicest thing is that you'll be walking somewhere and someone will just touch you on the shoulder and say 'I love the show,'" says Mary diplomatically.

"You've got to watch what you put in your shopping basket, that's for sure," adds Paul.

Has he ever been caught out? "Pork pie," he says, dolefully.

We meet on the day of Bake Off's final, in which 7.2 million viewers saw law student John Whaite triumph with a towering chocolate chiffon cake. Paul, 46, with his steel-grey hair and piercing blue eyes, has already become something of a sex symbol (the baking woman's crumpet, if you will). Mary, 77, is a bona fide fashion icon – when she wore a £29.99 silk bomber jacket from Zara on screen, it flew off the shelves and similar ones were being sold on eBay for £200.

"I think it's hilarious really," she says. "I mean, I just buy what I like. And all the scarves I wear are purely because I have a scraggy neck."

They can barely go anywhere these days without getting mobbed by amateur bakers asking for advice on the moistness of their lemon drizzle cake. Paul has even been recognised while standing at a urinal.

"They want to shake your hand, which is not ideal really."

Mary gasps. "No!" she says, half-shocked, half-delighted at the thought.

They make an unlikely double act and yet something about the two of them together just works. Watching them argue playfully on screen or in person is both entertaining and somehow reassuring, like eating hot buttered toast in a perfectly heated bubble bath. BBC bosses are aware they have struck TV gold – The Great British Bake Off Christmas Masterclass will be on BBC2 over the holiday period, and next year, Paul is embarking on a mysterious "solo project" while Mary is making two programmes about her life.

"It's terribly difficult trying to remember what you did when you were little," she says.

Paul interjects naughtily: "Especially before television in 1820."

She taps him sharply on the leg.

Both will spend Christmas with their families, eating turkey with all the trimmings. It is, one imagines, the first bit of peace either will have had for a while.

Paul has already made his Christmas pudding. "The secret is the moistness," he says. "I like alcohol but it has to be cooked out. The last thing you want is to have too much of it because it takes your breath away, takes the flavour away from anything that you're trying to eat. And a good mix of fruit. I like lots and lots of sultanas in mine and the sixpence has got to be in there as well."

It is knowledge like this – unpretentiously expressed, easily shared – that made Bake Off, presented by Mel Giedroyc and Sue Perkins, so watchable. It helps that, unlike some primetime talent show judges, Paul and Mary know what they're talking about and care enough to want to communicate their knowledge to a wider audience.

Paul is a former head baker at the Dorchester, born and raised in Wallasey, Merseyside. Mary is the daughter of a former mayor of Bath. She has written more than 70 cookery books and received a CBE in October. The success of their Bake Off pairing relies in part on these complementary differences: he the straight-talking Liverpudlian and she the kindly rosy-cheeked grandmother we'd all like to have.

"But basically we think alike – we want to achieve the very best baking," says Mary. "It's got to be the right texture, the right flavour, it's got to look good, to tempt, the crumb's got to be right – everything's got to be right. And they [the contestants] also have to follow what they've been asked to do. But within that, they've got to be creative and individual."

They've also got to avoid the baker's nemesis: the soggy bottom. "To me, soggy bottom is not acceptable and it spoils the whole of the bake," says Mary briskly.

Paul is generally the sterner critic. In the three series of Bake Off, he has caused more than a few wobbly chins. Does he feel guilty when he upsets people who have poured their body and soul into a flabby beef Wellington?

"No. I'm not having a go at them, I'm having a go at the bake. I'm not being horrible, it's constructive. They can disagree with me." Pause. "They're wrong, but they can disagree with me."

Still, if Mary disagrees with you, you wouldn't think she was wrong? He laughs. "It comes down to opinion."

Mary pats him on the knee. "He is difficult," she says fondly, as if talking about a mischievous child. "But we respect each other. I would never argue with him over a loaf of something because he knows the science of it, how they've achieved it and everything."

Paul: "I'll argue with Mary over every cake she makes."

Mary [rolling her eyes]: "Oh yes, he'll argue with me."

And yet they get on famously – Paul will stay at Mary's pied-a-terre when he comes to London from Kent, and they obviously enjoy teasing each other remorselessly.

"I took Mary to a drive-thru McDonald's yesterday," Paul says at one point. "Yeah, she loved it. Big Mac, large fries, six chicken nuggets, barbecue sauce, strawberry milkshake, a Dunkin' Donut..."

Mary: "I had nothing!"

Paul: "… and then she went back for an apple pie."

Neither of them is entirely sure why The Great British Bake Off has been such a success – the format has already been sold to eight countries, including Sweden which, Paul says, has the best-looking contestants.

"There's no one thing," he continues. "It's a sum of its component parts. You take out one of the cogs and it wouldn't work. It's a mixture of everything – so many different elements, down to the music, the setting, the tent, the bakers, Mary Berry, Mel, Sue, me, the challenges, the contestants – the whole thing together with the atmosphere, with the British countryside, even with the rain, it works."

There is a gentleness to it that is deeply appealing, as well as a sense that baking represents far more for the contestants than simply eggs and flour in a tin. There was a moment in this year's final when Brendan, a hot contender for the title, became speechless with emotion trying to explain why he had been inspired to bake a "family reunion" cake. It was an understated scene and all the more powerful for it.

"The whole show is totally honest," agrees Mary. "It's not hyped up, we don't want people to cry… it's a totally true programme and people make friendships among all the bakers. And if you look at them, as they're baking, they're never cross with each other – they're sympathique. I think it's lovely."

Paul: "I think baking's far easier than cooking, and because of that it's more approachable."

Mary: "Rubbish! Honestly."

Paul: "Making cake is one of the easiest things in the world."

Mary [vociferously, shaking her head]: "He's very grumpy isn't he? No, I don't agree with that. I think baking is very rewarding and if you follow a good recipe, you will get success."

One thing they do agree on is that they would like to see home economics become part of the national curriculum. "It needs to be put back on so that people have a basic understanding of what we're eating," Paul says. "It makes a huge difference."

"Particularly as the country is obese," Mary adds.

"Yes it's a fat country!" Paul laughs, then slaps his own stomach. "Says Mr Slim here."

Will they be signing up to a new series of Bake Off? For a few seconds, there is an awful silence.

"I'll be doing it," Paul says finally.

"We'll be there," adds Mary brightly. "The team will be there."

A nation of bakers breathes a sigh of relief.

• Try Paul and Mary's Christmas recipes

Click to buy Mary Berry's Baking Bible and How to Bake by Paul Hollywood at a special price from the Guardian Bookshop