High Street, Gosforth, Newcastle-upon-Tyne. Early March. Really, it ought to be raining, but instead the Greggs sign – four orange squares on a blue background – is bathed in sunshine. They say you should write what you know and, at last, my career has brought me to a wall of hot baked goods. I join the back of the lunch queue and ponder my options. As ever, it is hard to look past the sausage rolls. And, as ever, the first bite dispels any suspicions about their precise composition. This rich, golden experience costs 80p. The flat white I wash it down with is only £1.75, 40p cheaper than Pret a Manger, and just as tasty.

The atmosphere is friendly, the customers varied. Prams jostle for parking space by the loos. Older couples idly stir tea. Retired nurse Denise Massey (ham and cheese baguette, coffee) has popped in between acupuncture and pilates. Finance director Chris Alete (toastie, salt and vinegar Squares, sausage roll) is in the area on business. Seventeen-year-old Deni Stafford (toastie, chilli heatwave Doritos, Dr Pepper) is on a lunch break from her job at the hairdresser round the corner.

Britain is a Greggs nation, and the preeminent high-street bakery has had a good week. On Tuesday, it announced a 25% rise in pre-tax profits, to £73m, on sales of £835.7m. This is no flash in the pan: last year, profits for the first six months rose by 51%. The share price rose on the latest announcement. Cuts were announced, too. Three of its 12 main bakeries will be shut, with 335 jobs potentially lost, but the company stressed that this was part of a broader £100m plan for expansion – and, at any rate, 1.7% of its roughly 20,000 employees does not seem swingeing. Greggs has 1,698 outlets, more than McDonalds’ or Starbucks, and plans to take this figure beyond 2,000. It shifts more than 2.5m sausage rolls per week, and 1m cups of coffee.

The figures were a triumph for CEO Roger Whiteside, a veteran of Ocado and Marks & Spencer, who was hired in 2013 and set about repositioning the bakery as a “food-on-the-go” brand rather than a “take-home” bakery. “We realised we weren’t going to win the battle against the supermarkets for the take-home baked goods,” he tells me. “Instead, we had to deploy our bakery skills to sell our products for instant consumption.”

A flat white from Greggs costs £1.75, 40p cheaper than Pret a Manger. Photograph: Mark Pinder for the Guardian

This means sandwiches, soups and salads rather than just loaves and cakes, and a range of healthier options, too. The lower-calorie range now accounts for 10% of sales, and the figure is growing. “Everybody pops into Greggs for something at some point, but often that’s because they’re treating themselves. What we’re saying is: we want to be there for you, for breakfast, lunch and snacking.”

Greggs has 1,698 outlets, more than McDonald's or Starbucks

Gosforth is the Greggs ground zero. It was just down the road that John Gregg inherited a family yeast-and-eggs business in 1939, delivering baked goods by bicycle before opening the first shop in 1951, on Gosforth High Street. The original store was bought by a travel agency, which remains today – in a back room, staff showed me the outline of where the Greggs oven once stood. John’s sons Ian and Colin took over the business before John’s death in 1964. In his book Bread: The Story of Greggs, Ian Gregg explains that he was inspired by the early-20th-century Italian economist Vilfredo Pareto, who he came across while studying at Cambridge. Pareto observed that, in Italy in 1905, 20% of the people owned 80% of the land. His rule states that, in any field, 80% of the effect can be achieved with 20% of the effort. Gregg realised that by installing small ovens at the back of the shop and doing most of the heavy baking off site, he could achieve most of the theatre – the sights and especially smells of the process – without the hassle of a full-size setup. The brand quickly expanded, assimilating other bakeries along the way. It went public in 1984. In May 1994, it bought the Bakers Dozen chain, doubling its presence overnight. As Greggs grew, it brought its disparate shops together under a single brand – ditching suffixes such as “of Gosforth” and “the baker”, but retaining its honest image.

Listening to Whiteside’s breezy patter, it is tempting to see Greggs as a microcosm of battles being fought across the country: between green juice and meat pies; global conglomerates and family businesses; London and the north. Greggs’ northern identity is intact: at the Gosforth branch, the menu asks if you want to take your food away or “sit in”. “The culture is very special,” says Whiteside, “and a lot of that comes from the roots in Newcastle.” Newcastle is awash with Greggs, including branches open late into the night, and one protected by a bouncer at weekends.

Whiteside says central London is the only place where Greggs has a limited presence: rents are simply too high. “Our average transaction is £2.70,” says Whiteside. “You need a hell of a lot of customers to make that work where you might be paying £250,000 a year in rent.” While banks imperil the world economy with risky leveraging, Greggs is debt-free. It contributes widely to local charities and community projects, but still pays an annual dividend to shareholders. Staff are paid above minimum wage, with above-inflation rises and a healthy profit-share scheme – last year all 20,000 employees received a bonus of £500. The assistant manager at the Gosforth branch, Susie Brewis, told me she had been with the company for 19 years. When speaking about the profit share and the 50% staff discount card, she practically beamed.

The average transaction at Greggs is £2.70. Photograph: Mark Pinder for the Guardian

Business-wise, the company seems to combine a conservative approach to product with an open-mindedness about new ideas. “We watch all the food trends,” says Whiteside. “And, in time, if some of the things that are gathering pace in London become universally popular then, yes, we’ll consider it.” They recently introduced a katsu curry pasty, which has been selling well, but are waiting to check that sushi is not a flash-in-the-pan fad. “The other one I constantly joke about is quinoa,” Whiteside adds. “Trendy restaurants have quinoa all over the place, but we don’t think the British public is ready for it yet. We allow these more fashion-led places to go first, and then follow if there is demand.” There is also a high level of regional variation: you won’t see a stottie south of Thirsk.

Yet the company has taken risks and failed before. Under one of Whiteside’s predecessors, Greggs tried to launch in Belgium under the brand “Engelse bakker” before retreating in 2008, in what one paper called a “Dunkirk moment”. Early attempts at healthier options were slow off the ground. A trial of Greggs Moment, a coffee-shop-style brand with extensive seating, also failed, although its legacy is visible in the shop designs, which are increasingly trendy. In Gosforth, there is plenty of exposed brick, an old delivery bicycle mounted to the wall, and excellent i-fi.

Trendy restaurants have quinoa all over the place, but we don’t think the British public is ready for it yet Roger Whiteside, Greggs CEO

The surprising celebrity fans help. In 2002, the actor and model Milla Jovovich, a woman without outward indicators of a doughnut habit, said she would be happy to become the face of Greggs. The actor Thomas Turgoose is a fan, revealing in a 2010 Guardian interview that his girlfriend worked in a branch in Grimsby. Last year, Cheryl Fernandez-Versini launched her own Greggs chocolate bar for charity, and Jake Gyllenhaal said that his favourite pastime in the UK was to sit outside with a Greggs baguette.

Even the Observer’s food critic, Jay Rayner, concedes that Greggs is a canny operator. “They manage to have a very utilitarian high-street presence disguising a rather staunch commitment to a quality product,” he says. “They have been committed to short supply chains. It’s good stuff, with the caveat that you are talking about massive amounts of carbohydrate.”

Obesity is the elephant in the room. All but one of the diners I spoke to couched their love of Greggs in an acknowledgement that it was not the healthiest option, and said that they only stopped by once or twice a week. There are traffic-light labels on all the products, and the company is clear about the calories and fat in its products. But the transparency is only superficial, and the FAQ on the website is full of dead ends. It says that prices vary across branches, but won’t say which is the most expensive or cheapest. (Our investigations team can reveal that on the Seven Sisters Road, Islington, a sausage roll is 90p, 10p more than in Gosforth.) It confirms that the pure palm oil it uses is sustainable, and that it is “working on” ensuring sustainability across the supply chain – which invites the question of whether the combined fats it uses might contain the unsustainable variety.

The Gosforth branch of Greggs. Photograph: Mark Pinder for the Guardian

And the “freshly prepared” food that it trumpets is different from being freshly made. Although the bread is finished off in store, it arrives frozen. Assistant manager Brewis told me her life had been made easier by the advent of pre-chopped sandwich fillings and salad ingredients. Another former employee agrees: “The Mexican chicken sandwiches were a ’mare.” In a Guardian piece from 2010, a former employee recounted sprinkling the loaves with powdered egg to help create an even glaze, and loading lettuce “drowned in chlorine” into sandwiches. Greggs reveals its exact ingredients only on demand. The cheese-and-vegetable pasty recipe its office sends me makes it clear why: there are more than 50 ingredients, of varying familiarity. Hydroxypropyl methyl cellulose, anyone?

Greggs knows its customer base better than most other retailers Helen Colley, food consultant

While the fondness towards the company from staff and customers alike seems to be unforced and universal, there’s no doubt Greggs is helped by a well-greased PR machine, too. A few years ago, an error on Google caused a spoof Greggs logo to flash up with the overlaid slogan: “Providing shit to scum for over 70 years.” Rather than get angry, Greggs replied with grace and charm, offering Google doughnuts if the problem was fixed. Equally, the pasty-tax fiasco allowed Greggs to position itself as the embattled northern charmers against the evil, cash-sucking Tory government. The proposed tax was not aimed at punishing pasty lovers, but partly at levelling the playing field. Some of Greggs’ competition – fish and chip shops, for example – have to pay VAT. It is hard to feel too sorry for Greggs’ new competitors such as Pret a Manger or Eat, but high streets up and down the land are littered with the ghosts of old local bakeries killed by Greggs’ power.

“Everybody in the industry is watching Greggs, because nobody can quite believe how well it has done,” says Helen Colley, a food consultant who works on cakes for Nando’s and Costa. “Greggs knows its customer base better than most other retailers, and it adapts to demand. It sticks by its principles, and it makes things you want to go back for. It’s great value, but it doesn’t taste cheap. And it is honest. The packaging is simple, and it doesn’t pretend to be healthy. There aren’t any low-sugar cakes. The presentation says: ‘This is a great big slice of cake and, if you eat it, you are going to enjoy it.’

“There are plenty of little artisan bakeries doing sourdough and avocado and things, but no traditional ones. Greggs is completely on its own, forging ahead.”

Back at head office, Whiteside is preparing for the next expansion. The rationalisation this week is about creating “centres of excellence” – a euphemism for factories specialising in one or two products, rather than making a bit of everything. Greggs’ new focus is on non-high-street sites: hospitals, industrial estates, office parks – places where there would not have been demand for a bakery, but there might be for baked goods on the go. In 2014, it was reported that the New Cross Hospital in Wolverhampton, where 70% of the population is obese, had the second-busiest Greggs in the country, which the local NHS trust boss described as “not ideal”.

Choosing a site is as much art as science, says Whiteside. “We use all the data, of course, but there’s no substitute for boot leather. You really need people who know the area. It can be as simple as being on the right of a crossing, not the left. But anything near a bus stop is good news.”

The first Greggs-branded shop in Northern Ireland will open soon in Belfast. Beyond that, Ireland would be the logical next step. Once all of the UK stores are up to scratch, who knows? Will Greggs take pasties (no longer “Cornish”, since EU regulation in 2011) to Japan?

“I don’t think we’ll rush into that market, no,” says Whiteside with a chuckle. “Never say never. But our brand is doing the common uncommonly well. And a big part of our positioning is that we’re market leaders in pasties and sausage rolls. Those are products that only the UK eats.”

As ever, it’s hard to look past the sausage rolls.

• This article was amended on 5 March 2016. Belfast was incorrectly placed outside the UK in an earlier version because of an editing error. The article was further amended on 7 March 2016 to correct a percentage miscalculation; 335 jobs out of 20,000 is 1.7%, not 0.26%.