The year, 1999; the place, Hoxton Square – though you wouldn't know it, were you to take a time capsule back from today's East End. Instead of Smokey Tails, imagine a pie and mash shop; instead of Happiness Forgets, a small, shady nightclub. Imagine ramshackle buildings, the majority boarded up with 'Do Not Enter' signs.

"You had more chance of finding five grams of smack than five kilos of tomatoes," chuckles Theodore Kyriakou, "but we could afford it, and it was south-west facing" – an aspect favoured by Greek restaurants because it means they face the sunset. I can't imagine there was much of one in Hoxton in the 1990s – but one thing is certain: metaphorically the sun did not set on The Real Greek.

The chain – now nine outlets and counting – has changed considerably since Kyriakou sold it to mass caterers in 2007, but under his watch it offered a rich, sun-drenched glimpse of what Greek food could be. People had their reservations back then, of course: about the concept of sharing plates (unheard of at that time, hard as that is to conceive now) and even about the food itself, which was not the moussaka and garlic bread they knew and understood, but arnaki me maratho – rack of lamb poached with fennel; kaltzounia me mizithra – small tartlets made with cottage cheese, and other fresh, vibrant ingredients we didn't know to be Greek. "Some people walked out when they realised we didn't have moussaka and chips," Kyriakou remembers, but those who stayed witnessed the birth of a movement which, almost 20 years later, is coming to fruition: of modern, produce-led, indigenous-chef created Greek food.

"Only five years ago this would be a different conversation." I'm talking to Télémaque Argyriou in the sunshine outside his street-food van serving 'extra virgin' Greek food. The scent of lamb gyros and halloumi drifts over us on the grill-warmed breeze. Five years ago the Real Greek was around, but in the wake of Kyriakou's sell-out had reverted back to the failsafe staples of 'Greek' as the British perceived it: what Kyriakou has since described as "a mish-mash of Turkish, African and Cypriot cuisines."

"I used to struggle to find good examples of Greek cuisine in London, basically" Argyriou says. "Now I can name several – Mazi, Opso, Greek Larder, Gourmet Goat – but back then it was all comfort food."

For as long as we'd had them, so-called 'Greek' restaurants in London had been dominated by Greek-Cypriot cuisine – or at least a version of Greek-Cypriot, brought over by Cypriot migrants and refugees who fled to London during the civil unrest of the 1960s and 1970s. "To sell cheap, comfort food like chips and moussaka was an easy win," suggests Kyriakou. They were looking for money, not an opportunity to showcase their food culture – "and besides," he continues, "Greek-Cypriot restaurants are to Greek cuisine what the Bangladeshi restaurants people referred to as 'Indian' in the nineties are to today's Trishna or Dishoom. They are simply very different cuisines."

It used to be a struggle to find good Greek food in London, but not now

It's a refrain I hear repeatedly from the producers, chefs and entrepreneurs behind the growing Greek food movement. Their frustration is not with Cypriot food per se, but with the effect it has had on our perception of Greek cuisine. "Even the holiday food in Greece did it an injustice," laments Yannos Hadjiioannou of Maltby and Greek, one of the movement's most pioneering figures. He imports Greek produce – both the expected and the eclectic – which he sells to restaurants and delis from his small shop on Maltby Street in Bermondsey. Everyone in the restaurant world knows him; the majority use his produce, even if they are not actually Greek. "Some of the top restaurants in London I supply aren't Greek," he says on the phone, in a muffled tone as he unloads his latest consignment of tomatoes – the very same tomatoes (I like to think) which a few days later I am enjoying in Argyriou's koulouri bagel. "Bagel?" I mumble quizzically through a mouthful of thyme-infused scrambled eggs and tomato. His reply is almost indignant. "Yes, they do have bagels in Greece!

"It is bagel to you, but in Greece it is koulouri – there's a large Jewish community in northern Greece," he tells me, and inevitably, a Greek version of this Jewish roll has emerged over the years. "It is soft and slightly aniseedy on the inside, and the outside is crisp and covered in sesame seeds," Argyriou explains. It's the first of dozens of ingredients to surprise me during the course of my miniature odyssey around London's 'new' Greek food: pasta, truffles, rice pudding and grape molasses soon follow, along with tea gathered by hand by elderly women from the mountains, and kritama, a sea herb I sample at Greek Notting Hill restaurant Mazi.

"The kritama grows on the rocks by the sea near my father's home in Greece. He sends it over when he can get it," says Mazi's co-founder Christina Mouratoglou. Born in Thessaloniki, Mouratoglou is another young Greek foodie determined to wrest control of the identity and future of London's Greek food. "We had no Michelin stars here. Every other cuisine, even those with less-than-unblemished reputations like Chinese, had Michelin stars," she recalls herself thinking, back before she opened Mazi in 2011. She saw the potential, both in the food and in the chefs, to get one.

Love it though they did, the Greeks had never really capitalised on their sumptuous produce: truffles went untruffled, family olive groves overgrew and vines were left untouched – a result, in part, of Greece joining the European Union in 2001, claims Kyriakou. "We left the land, and abandoned things like that for the cities after such a large influx of money" he says bluntly, "only now the shit has hit the fan, young people have gone back to the land of their grandparents and parents to see what they can do."

The answer is: plenty, as evidenced by Argyriou, whose family olive grove is not just the company's namesake, but its main supplier of olive oil. "Kalimera oil has been in the family for 200 years, but we'd never used it for anything other than our own purposes until I decided to bring it to the world." He's joined by a heavenly host of young Greek winemakers, apiarists, cheese and pasta makers like Yannis Georgakopoulos, who, after studying accounting in Athens, decided to return to his hometown of Andritsaina in the Peloponnese mountains to make pasta based on age-old recipes unique to the area, using local eggs and milk.

Maltby St's Greek deli Maltby & Greek

Maltby St's Greek deli Maltby & Greek

In historic times, pasta was made by the old village women, who would lay it out under the sun for days, explains Hadjiioannou, who imports the funny square hilopites, along with various other varieties of Georgakopoulos' pastas, and a plethora of other products. The merit of youthful producers, he continues, is that they are well educated – often beyond university level – and entrepeunerial. "We can help them," he continues. "They know the importance of things like branding, the internet and so on, and they want to learn. They want to make their products work as a business." He cites his young supplier of aubergines and tomatoes as an example. "You can build good relationships, because they'll put in the time and effort that's required."

It has not always been this way. Marianna Kolokotroni of Olivology started selling artisanal produce – oil, honey, truffles and nuts – from Greece in Borough Market back in 2009, when Greek food still basically meant hummus and pitta. "It has been a long journey making relationships and training producers," she says from her newly expanded and richly stocked stall. "The quality of the products was always very high, if you were looking in the right places, but the communication and logistics were not as easy." Dealing with older producers, who were used to getting their own way, was a challenge, she continues, but this is changing with the new, more "open-minded" generation. "It took us quite a long time (compared to our Italian cousins) to create a buzz about our food, but we are getting there… Not only because chefs such as Jamie Oliver or Rick Stein have been so passionate about Greek cuisine."

I Google it – and sure enough there is Jamie singing the health benefits (which are legion) of Greek cuisine alongside recipes for skordalia, kakavia and potatoes yiachni. Followers of Rick Stein's series on the Mediterranean last year, meanwhile, may well remember the episode he spent tasting his way around Greece. The final scene saw him tuck into pot-roasted goat with potatoes, artichokes and fennel: the sweet aniseed of the bulbs melding with the meltingly tender meat. He is impressed – as indeed many have been recently, by the meat's inimitable taste. Gamey, floral, and evocative beyond its years, goat meat in Greece does not mean the tough, stringy slabs of old goat found in less salubrious butchers, but kid goats: young males who, though clearly useless in the way of cheese and milk production, have long been valued for their meat.

It's taken a long time to create a buzz about Greek food, but we're getting there

So far, so sensible – yet what in Greece and much of the Middle East and Asia has long been common practice has in Britain been a rarity until recently. Moving to London to study after growing up in the Mediterranean, Nadia Stokes of Gourmet Goat was dismayed to discover how hard it was to source her favourite meat. Goat's cheese, easy. Goat's milk, increasingly so. But male kids, far from being prized, were being euthanised and burnt at birth on the assumption there was no demand and they were a drain on resources: an assumption which, thanks largely to her and her husband Nick Stokes' pioneering street food stall, has since been disproved.

In May, the Gourmet Goat received one of the BBC's coveted Food and Farming awards: a significant victory, and not just for goat-meat consumption. Stokes' selection of goat dishes had people queuing 20 or 30 deep in Borough Market – but it wasn't just the pungent meat, slow-roasted with thyme, lemon, garlic and oregano, and cushioned in soft pillows of pitta with creamy tzatziki, the devotees were greedily devouring. "Most of our core side dishes, including wheat berry salad, flash-pickled kohlrabi with feta and pomegranate and roast dakos salad are made up of core Greek ingredients," Stokes explains, "and we've had such a positive response." For the first two years they had to explain each one. "We spent an inordinate amount of time explaining every ingredient and process," she recalls. "We seem to be doing that less now. I think it has become quite clear to us that there is a lot of appetite for new Greek dishes, or at least a better expression of the cuisine." Her hope for the future of food served from Greek restaurants and street vans is for "more regional representation, less chip-filled souvlaki."

This sentiment is echoed – and indeed rewarded – by Mazi's Mouratoglou, whose menu reflects the myriad regions represented by her kitchen staff. "The barley rusks which come from Rhodes in northern Greece we have in our Greek salad. Our orzo pasta giouvetsi with braised milk ossobuco and mizithra cheese flakes is from the south, near the home our head chef." So diverse are the regions that quite often "I'll suggest dishes the chefs have never had before and vice versa." Greece is blessed with many landscapes – and an eclectic gaggle of neighbours. There's the Balkan states, Italy just a spit away from the Ionian islands and Turkey, of course, for whom Mazi's politiki is to thank. After all, as Kyriakou bluntly remarks, "we spent 400 years under the Ottoman empire. It would be impossible to think Turkish men and Greek women didn't occasionally mix."

This fusion continues. Many Greek chefs come to London via the kitchens of South America, northern Europe and Asia – particularly Japan, Kyriakou informs me, where there are growing numbers experimenting with Greek and Japanese cuisines. The effect can already be seen in Mazi's grilled aubergine, soy and thyme honey dip, served with warm pitta as part of a mezze. The moussaka is made with shitake mushrooms. "This is modern Greek food. Every dish on the menu comes from a traditional recipe – we don't make stuff up – but we give it a twist," says Mouratoglou. "When it comes to tasting it, my test is if I shut my eyes, can I imagine that I am in Greece?"

Every Michelin-starred restaurant in London has a Greek cook

It has to taste authentic: a hackneyed word in the food world, but among those chefs, cooks and restaurateurs trying to rebrand Greek cuisine today it seems paramount. "The Italians have done very well at working on the image of their cuisine without alienating it," says Argyriou, "and we have to do the same." As such, where most restaurant kitchens in London are melting pots, almost every chef at Kalimera, Mazi and Opso, Marylebone's modern Greek restaurant, hail from Greece. Freeze-drying, sous vide, smoking, molecular and mousses suffuse their menus: "for our giouvetsi" – a traditional dish of grilled lamb cooked with pasta – "we cook the lamb sous vide for 15 hours at 64˚C, then separately cook the orzo with lemongrass before bringing them together with tomato jam. We have Greek customers who say, 'It doesn't look like giouvetsi!'" grins Opso's founder Andreas Labridis, "and then they try it." They might not make taramasalata like their mothers or grandmothers, he and Christina say of their kitchen team, but they do need to understand Greek food.

The odyssey continues. Victory shifts, as Homer so sagely observed in that most famous Greek work, and just as some of Britain's most pioneering food businesses were born of our 2008 crash, so from the ashes of Greece's debt crisis are rising producers and chefs of sparkling verve and creativity. "Every Michelin-starred restaurant in London has a Greek cook," Mouratoglou claims. Greek spending on clothing, household items and other luxuries might have dropped in recent years, but their native love of food and drink remains undaunted. "We will find any excuse," Hadjiioannou grins. "You might not have a job, you might be struggling for rent – but you will always find €10 somewhere for a glass of ouzo and a mezethes" – and if that's not a recipe for culinary greatness, I don't know what is.