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It’s perhaps fitting that my meeting with Paul Hollywood and Nigella Lawson coincides with the kind of sweltering, high-summer temperatures that have long been The Great British Bake Off’s meteorological signature. Heat that melts chocolate, fritzes mixing stands to malfunction and liquefies baked Alaska to the point it has to be chucked in the bin. Heat that prompts overwhelmed amateur bakers to put dampened tea towels around their necks, sweat through aprons and flap haplessly at cakes that refuse to cool.

Such temperature is in abundant supply as I make my damp-browed way through the airless, oven-door humidity of a west London studio complex on a 35°C heatwave day. Fans and cooling equipment are, apparently, in short supply in the building. And so, as I’m led into a little hair- and make-up room, it’s perhaps not too surprising to find Hollywood huddled beside a portable air-conditioning unit, while Lawson is sprawled out on a sofa, just a toga-wearing grape-bearer away from the full Cleopatra.

There’s plenty to talk about – Lawson’s internet-breaking announcement as Bake Off’s newest judge; the much-discussed matter of her chemistry with Hollywood; the other fascinating, wholly unprecedented twists that the show is introducing as part of its 17th series. But, given the circumstances, it makes sense to start with the heat. Lawson has previously discussed her natural aversion to boiling summer weather and, on meeting her new colleague Noel Fielding, she jokingly said that there would now be “two goths on the show”. So how did she cope making her debut during a summer of record-breaking temperatures that presumably gave new meaning to the phrase “baptism by fire”?

“We were just getting hotter and hotter, as you’d expect, and because it’s The Great British Bake Off, it’s delightfully British with not an air-conditioner in sight,” she says in her trademark velvety burr. “It was all great. I walked everywhere with a parasol.” And did your fellow judge ever hold it for you? “I did a couple of times,” says Hollywood after a pause. He adds that there was a point towards the end of the shoot when his son, it seemed, helped fan Nigella down. “He was employed as the fanner,” says Hollywood, with a little smile and a mischievous glint in his icy blue eyes.

Hotter still, though, was the news of Nigella’s appointment itself earlier this year, in what must be one of the biggest TV coups in recent memory. Following Prue Leith’s announcement in January that she’d be leaving the show after nine years as a judge, much of the early speculation about her possible replacement swirled around figures like Nadiya Hussain, Lorraine Pascale and Leith’s friend and occasional on-screen deputy Caroline Waldegrave.

However, from the moment that Lawson – mononymous domestic goddess, bestselling author, global TV icon and legitimately one of the most influential British cooks of the last 30 years – emerged as a frontrunner, the general tenor was that this was a televisual match made in heaven. Official confirmation that she was joining the show, and implicitly giving it an invigorative boost after 16 years on the air, unleashed a kind of disbelieving glee (The Guardian: “a piece of blessed news equal to three or four regular pieces of good news”). As Hollywood himself puts it, a little later in our conversation: “We’ve got Nigella Lawson on the Bake Off. End of story. Exclamation mark.”

So how did it feel for Lawson herself, to be joining the show aboard a tide of such goodwill, surprise and expectation? Beyond a role alongside the late Anthony Bourdain on short-lived series The Taste, joining a cooking show as a full-time judge is uncharted territory. Was there apprehension?

“I felt it was a huge leap, but it’s been lovely,” she says. “I was a bit worried because, well, you wouldn’t mark me up for my polished finishes as a baker. Generally speaking, I don’t think of myself as a judge. But I spoke to Paul, and we got on.

“I came to baking later in life and because of that it’s something that intrigues and fascinates me. I’ve learnt by doing and I’m a home baker, not a professional. It’s quite interesting because the contestants are home bakers, too, so I have sympathy for that. But, also, I just love seeing them sparkle.”

This is abundantly clear right from the first episode of the new series – an irresistible, 90-minute confection that deftly rejuvenates the show and slots Lawson’s vivacious, verbose glamour and camp into proceedings with such seamlessness that you struggle to imagine what Bake Off was like without her. And it’s all anchored by the apparent personality contrast between her and Hollywood – he the Cheshire-born second -generation baker who is all controlled, steely-blue gaze and forensic analysis; her, the Oxford graduate, journalist and daughter of a former Chancellor, who memorably goes back to a slice of coffee and walnut cake for one last, indecently huge bite – and the unavoidably flirtatious, fondly needling chemistry that comes from it.

So what was it like for him, the lone ever-present across the various judging and hosting line-up reshuffles of the show’s history, to work with Nigella, having previously established relationships with Leith and Mary Berry? And should she cover her ears to protect from embarrassment or otherwise? “Oh, I’m used to not listening to him,” she pipes up, with a laugh.

“The thing is,” Hollywood begins, “Mary was different to Prue, Prue was different to Nigella and Nigella is different to Mary. They each bring their own character to it, and Nigella is a very warm person, especially to the bakers. More so than Mary was and I think more akin to Prue. There’s a very nurturing nature to Nigella, which was quite strong this year. Whereas me, I suppose I’m the constant. So I remain in my position of being constructively critical.”

Lawson nods in agreement. “I think you are the backbone of Bake Off, and that allows people with different personalities to come in, whether it’s another judge or [new] hosts, and I think you need that continuity because you need to be consistent as a baker and as a judge,” she says.

“The bakers learn from Paul and I do as well. He only pretends to be very unsmiling but, in reality, he’s got a real twinkle and he’s really lovely to tease. He takes it and he can hand it out.”

The pair’s camaraderie seems to have manifested through jokey backstage conversations with hosts Noel Fielding and Alison Hammond, plus Lawson’s apparent habit of supplying the quartet with snacks, zip-lock bags of sweets and, on one occasion, a big cheeseboard. “We all sat in the hotel with this plethora of cheese and crackers and loved it,” says Hollywood, with a grin. “Nigella is 100 per cent a feeder.” “And an eater!” she adds, sitting up from her prone position to make this important distinction.

Intriguingly, Lawson is not the only new ingredient added to Bake Off’s patented formula this year. As well as “wearable” bakes and a free-from week inspired by children’s parties, for the first time ever – as prompted by a request for ideas from viewers – bakers have to complete a signature bake alongside a relative they’ve invited to join them in the tent.

“I don’t like change,” says Hollywood, somewhat sternly. “I’m a traditionalist and I don’t like changing the format at all. But the audience choice of “bake with a relative” was a fantastic idea. The interaction, how they allocated work to their partner. It gave us a chance to be nosey.”

The same went for the free-from week, in Lawson’s opinion, because it afforded the opportunity to “look at things you’re familiar with in a different way”, and drove to the heart of the inclusive, eccentric wholesomeness that is so central to the show’s appeal. “This is a programme that really goes deep into the hearts of viewers,” she says. “They feel it’s their programme, too, and it really is.”

The flip side to this sense of ownership is that Bake Off is a gig that comes with heightened scrutiny, criticism and press visibility. Given Lawson’s fierce privacy and long service as an unwilling object of tabloid obsession (here we turn to the swiftly dismissed, pre-launch rumours about off-camera discord between the show’s new judging partnership), how does she feel about the intensified spotlight her new role might bring? “I don’t want to think about that,” she says. “I’m very happy having a totally private life and lounging about like this when I’m not working. So I just concentrate on doing it. I don’t want to consider what other people are going to think when it’s being broadcast. That wasn’t the allure of doing this work.”

Hollywood – who has done his own time navigating rabid press interest in his private life and relationships – describes these strains of Bake Off-mania as something of an occupational hazard. Particularly in the context of the show’s global syndication and spin-offs (including US version The Great American Baking Show and the celebrity-infused version in aid of Stand Up 2 Cancer). “It’s something you get used to and whether you like it or not is immaterial,” he says. “There are two places in the world that I have been to where I haven’t been initially recognised and they are Japan and Russia. Everywhere else, I’ve been recognised. And that’s because of Bake Off.”

You have to imagine that Lawson’s involvement (she has sold millions of books worldwide and has made regular guest judging appearances on Australian television as part of MasterChef and My Kitchen Rules) will only boost the show’s international renown. Yet, despite their outwardly opposed dispositions, it turns out that Lawson and Hollywood are kindred spirits when it comes to their relationship to fame. “I’m a bit like Nigella in that we tend to go away into our little holes and disappear [when we’re not working],” says Hollywood. “And then we just get pulled out of the box to do Bake Off before disappearing again.”

Given that, for Lawson, this is the latest shift in a career that has seen her work as a literary editor and restaurant critic, it’s worth asking how long she thinks she’ll keep getting out of that figurative box. Does she think she’ll be on Bake Off for the long haul and for many more series to come? “It’s not for us to decide,” she says, averring. “It’s for the viewers.” Hollywood smiles again and chips in. “I’ve said before that [the show] is like Hotel California in that you never leave. Nigella’s staying where she is.”

This may be true in a professional sense. But in a much more literal sense, she and Hollywood are about to move on to a final press engagement. One of the publicists raises their voice over the whirr of the air-conditioning to tell me it’s time to wrap things up. So: Bake Off has survived its transition from the BBC to C4, multiple tweaks to its hosting and judging line-up, plus a fractured, digital-age entertainment landscape that feels at odds with its hopeful, old-fangled vision of earnest bakers competing in a bunting-strewn tent. What do they put this down to?

“I think we need a show like Bake Off more than ever,” suggests Lawson. “Particularly in a hi-tech, fizzing, popping, shouty and often hostile world where we’re all on screens. In baking, you’re using your hands, using your senses and people are encouraging one another.”

They’re rousing final words, and so we end there with both of them rising to file out of the room, as Lawson notes that she needs to “pee” beforehand. “We’ll go and get the Shewee,” says Hollywood with a laugh, as Lawson rolls her eyes and gives him a playful nudge.

And there it is: the tonal mix of mischief and emotion, sincerity and silliness, that has made this show such a persistent, peculiar joy for more than 15 years. Nigella Lawson’s arrival may have slightly altered The Great British Bake Off’s recipe. But this lavishly iced institution feels as deliciously moreish as ever.

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The Great British Bake Off begins on Tuesday 22 September at 8pm on Channel 4.

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