A group of young men sit gathered around a plastic table in a tiny restaurant. In between them squats a small, square iron griddle above an open flame; a tube snakes down to a gas cylinder by the table legs. Under the men's laughter is the sound of sizzling, and the smell of cooking bacon fills the air.

On the face of it, friends enjoying a meal and a beer together on a Saturday night appears completely normal, but there's a difference between this and a weekend piss-up with your mates: despite the casual atmosphere, these men are wearing military uniforms and heavy-duty boots.

In London, this would be a rare sight. Here in Seoul, South Korea, it's business as usual (conscription is mandatory), and a stark reminder of the country's political situation and the ongoing difficulties with North Korea.

I watch them as they laugh and joke, using a pair of tongs to prod the food cooking on their barbecue. My reverie is broken by the arrival of a plate of food at my own table: raw pork belly, garlic, greens and kimchi, the spicy fermented cabbage that's currently all the rage in London.

"Put it all on the grill!" says Lee, my guide, enthusiastically. On goes the chopped-up pork belly; the rest of the ingredients all follow according to cooking time.

"This is one of Korea's most traditional dishes," says Lee. "You find it everywhere." He nods at one of the soldiers as they walk past to fetch a beer and a small bottle of soju, Korean rice wine, from the fridge.

Koreans always slice their food so it can easily be eaten with chopsticks; knives are considered weapons

I learn that Koreans always slice their meat – and most food – into bite-sized morsels that can easily be eaten with chopsticks, because knives are considered weapons and aren't part of a table setting. I also learn that Koreans are considered to be Asia's kings of beef, while Japan is known for fish and the Chinese for pork.

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With battered pink walls and spartan decor, the restaurant we're in isn't trendy. It lies down a backstreet called Pimatgol, just off the Jongno thoroughfare that leads to Seoul's main palace. The area itself is steeped in history; travelling along Jongno was tedious for the lower classes, who would have to bow every time a noble travelled past. To avoid this custom, they built a small alleyway running parallel to the main street – Pimatgol – that enabled them to avoid the nobility.

Since then, the alley has been used as a meeting point for the organisers of the Sam-il Movement the night before the Korean Declaration of Independence, and was a hiding place for student protestors in the 1980s. Today, much of it has fallen prey to urban development, but it's still largely a warren lined with traditional restaurants. The particular one I'm in is, erm, homely; no one speaks English and I'm pleased Lee is here because to be frank, I'm a bit intimidated by having to cook my own food.

I let him take charge, turning the ingredients with a well-practised hand while he talks to me and my friends about food culture in South Korea. Korean barbecue, along with the other dishes Lee namechecks, are the delicacies that we know best in London: fried chicken and beer (together known as chimaek), rice dumplings called tteokbokki, gimbap – a Korean take on sushi rolls and a relic of the Japanese invasion – and the rice dish bibimbap.

A street scene in Seoul, South Korea

If you're bored of Googleing 'Things to do in Seoul, Korea' and want to get a taste of the Korean classics in London, you can head to the likes of On the BabJinjuu and others. And given the cuisine's growing popularity several thousand miles away, you'd think that they were still going strong in their home country.

And they are – there are street-food stalls at every turn – but, Lee says, the old ways are on their way out. Many of the truly traditional street-food stalls are closing down; dining here is becoming more westernised, with familiar brands popping up all over Seoul, and people preferring to eat in restaurants.

"Starbucks was a success; McDonald's and KFC were not," says Lee, although he can't really pinpoint why. We walk down a street dedicated to restaurants that just serve craft beers and fried chicken – it's obvious to me why KFC didn't succeed.

Linda Lee, founder of London (and soon to be Paris) restaurant On the Bab, explains a little more: "Fried chicken has been popular in Seoul since the 1960s, and since then many different styles have evolved. Today the most popular style is yangnyeom, which is small pieces of twice-fried chicken, usually coated in a sweet and spicy or garlic sauce."

"The ease of eating and the strong flavour makes it the perfect accompaniment for beer and other alcoholic drinks, which is a big part of eating in Seoul," she continues. We hit another street, 8-Gil, in the Myeongdong district. The road is lined with street-food traders, each one specialising in one dish. I walk past places selling fish soup, blood sausage, carrot fritters – the variety is endless. Judy Joo, founder of Korean-influenced fine-dining London restaurant Jinjuu in Kingly Court, explains that Seoul has many 'one-trick ponies' that only serve one particular dish: "These places serve dishes that have that memorable sohn mat (taste of the hand), that makes dining in Korea so special."

Yet at just about every stall, there's one constant: kimchi. "Kimchi has existed for over 2,000 years and originated as a way of preserving vegetables. It guaranteed availability of healthy vegetables all year round before refrigeration, but also gives them a delicious, distinctive tangy, spicy flavour. It's essential!" says Lee.

Crab is served in Seoul, South Korea

Crab is served in Seoul, South Korea

In Gwangjang Market, I come across kimchi in my favourite form: dumplings, served with addictive chilli sauce. In Korea, spice is sweet and aniseed-y, rather than the kind that'll make you break out in a sweat.

Here, there are vats of kimchi – all different kinds – as far as the eye can see. It's made with different vegetables, different spices. "There are more than 100 different kinds of kimchi," says Lee as we walk past and I gawp. "And it tastes different at every stall because of the bacteria on the housewives' hands when they make it."

Judy Joo agrees: "Although it's most commonly made with cabbage, the word actually refers to a wide assortment of fermented vegetables and fruits, boasting over 187 official varieties. Essentially, you can 'kimchi' anything and every Korean family has their own bespoke recipe."

It might seem odd that so much importance should be placed on a side dish. But in Korea, the quality of a meal isn't judged on one thing – the banchan, or small side dishes, are just as important, to the extent that the best meals are considered to be ones where you can barely see the table for all the plates of food on it (something that, I later realise, probably stems from South Korea's long stretch of poverty). Hanjeongsik restaurants revolve around this style of eating: dozens of plates, large and small, arrive at your table: blanched veg with sesame oil; soybean and tofu soup; fresh leaves; cured seafood and more.

In Insa-dong, the arts district near the ornate palaces, we come across my favourite street food. It's a traditional dessert, made out of honey that's dried for three days and fermented for a week, until it becomes light grey in colour. It becomes hard, and is then mixed with cornstarch. The stall owner makes a hole in the middle and uses a special machine to magically stretch it until it becomes really stringy, "like a grandmother's white hair." Eventually, it gets to the point where there are 16,000 strings – I try to count but can't keep up. Peanuts or sesame seeds are placed inside, and it's made into thumb-sized pastilles, dusted in sugar. They look a little like smaller, fluffier, whiter Weetabix. I pop one in my mouth: it's nutty, sweet and chewy, and really, really moreish.

Street food in Seoul is always evolving; it's why I return there so often, to keep up to speed

Lee tells us that it was a treat reserved for the royal family, and that this is the only stall still making it in the traditional way. It's a bizarre contrast to the Shake Shack that we stroll past a few minutes later. Lee is saddened by the changing face of Seoul's traditional street foods. On The Bab's Linda Lee, as a Seoul native who lives in London, sees it differently: "It's a really vibrant market and there's such an appetite for new foods and concepts. Street food in Seoul is always evolving; it's why I return there so often, to keep up to speed."

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Judy Joo agrees. "Modern street food is dynamic and always changing. There are traditional dishes and a wide assortment of the wild and wacky latest food trends, like bibimbap waffles, foot-long bbq chicken skewers, extra-large hotteok (savoury or sweet stuffed pancakes) and baguette burgers (hollowed out baguette rolls stuffed with meat and cheese) but more classic dishes can still be found in buzzy markets and streets, mirroring traditional home cooking."

This is what strikes me more than anything about Seoul: it's a city hovering between old and new; between eastern tradition and western 'modernity'. Food is plentiful, there are stores selling pretty-looking tat everywhere, and shopping seems to be the primary activity. But, given South Korea was the world's poorest country until the 1960s, I'm not surprised. After the Second World War and Japan left, the country was divided in two. "North Korea is where all the natural resources are, and South Korea suffered," says Lee. "The traditional greeting was, 'Have you had breakfast?'"

I wonder if any of the northern food specialities are being lost. "Naengmyeon, a northern dish of chewy noodles swimming in an ice cold tangy broth, is super popular when the heat of summer strikes Seoul," says Judy Joo. "You'll find everyone slurping mountains of these noodles topped with slices of fresh cucumber, pear, radish and a boiled egg. I think that many family restaurants specialising in dishes from the north are really trying to keep these classic dishes alive and the tradition going."

A plate of classic Korean barbecue in Seoul, South Korea

But as much as traditional food reigns supreme in some parts of the city, Seoul also offers what Judy describes as "a glorious mix of old and new. The contemporary food scene in Seoul is about modern fusion food. Like Vatos Tacos, a Ko-Mex [Korean-Mexican] restaurant in the expat area of the Itaewon district. My friends and I usually go to nosh on kimchi carnitas fries late at night."

As much as I love kimchi and the other traditional specialties of the country, one of the dishes I like the most is an east-meets-west hybrid of tteokbokki rice dumplings topped with shedloads of melted cheese. And that's what Seoul and its food is all about: being creative, weirdly and unexpectedly brilliant, and paying heed to history and its traditions while being open to making new ones. My favourite case in point, from just outside the city, is when I'm told that in the DMZ (demilitarized zone), veterans and farmers are encouraged to grow organic crops – because of the lack of pollution. For me, this truly hammers home how the country's complex history has resulted in a flourishing and vibrant food scene.

These days, South Korea has experienced a wave of economic prosperity. It's one of the financial centres of the eastern world, and has consequently undergone vast swathes of development. There's a penchant for excess. Take, for example, the fact that until the 1970s, most of the Gangnam district – immortalised in Psy's song – was rice paddies and agricultural fields. Today, its streets are lined with designer shops.

Socioeconomic change at that speed and scale can be hard to keep up with, so it figures that there are many who consider Seoul to be a city that, in the modern day, struggles to define itself. I, however, think differently; I think Seoul knows exactly what it wants – everything, old and new, traditional and modern, all at once. And if that makes it confusing? Well, it doesn't really care.