On a bright Saturday morning in Havana's leafy Vedado district, the outdoor market on the corner of 17th and K streets was jam packed with shoppers. Trestle tables were lined up nose to tail, weighed down with fruits and vegetables. Mounds of mangos – more than seven kinds, each with a subtly different level of sweetness – sat next to piles of pineapple, limes and the sweet potato-like taro root. Rows of plucked chickens hung from strings, while carton upon carton of eggs were stacked almost to head height. There was the constant chatter of buy-and-sell, hearty greetings, jokes and laughter, as well as the occasional whispered offer from shifty men selling plastic bags of black-market potatoes and onions. At one end of the market, a sound system was blasting out Latino pop tunes, while sporadic announcements were made over the microphone.

“Oh my god,” said Tanja Buwalda, author of The Cuban Food Blog, who has brought me here as part of her newly launched Havana food tour. “That last announcement was telling everyone about the price of beans at one of the stalls. That's advertising – advertising does not happen in Cuba!”

At most markets around the world, the sound of stallholders shouting about their bargains is not exactly unusual. But in Cuba, one of the last holdouts of communism, the streets and buildings are (it must be said, refreshingly) free of billboards and posters. Public proclamations about the merits of your wares have been anathema here for more than 50 years – but things are changing.

Only a couple of years ago, the idea of a Havana food blog – let alone a guided “field to fork” city tour – would have seemed faintly ridiculous. Cuba has not exactly been known for its culinary delights. Strict state control over the food supply since the 1959 revolution, as well as tight restrictions over who could open private restaurants, has meant that only the plainest of ingredients – such as tasteless chicken, tough pork and rice – have been available, and nearly all of the country's talented chefs had to leave Cuba in order to cook freely. But over the past year or so, there has been a shift in the government's thinking: a glasnost in gastronomy.

Paladares – private restaurants that once operated out of people's homes – are now widely allowed to become proper establishments, meaning they can be bigger than one room, stay open later and be staffed by waiters, rather than family members. A small number of expensive private market stalls have also sprung up in public markets such as the one on 17th and K, selling previously hard-to-find vegetables such as carrots and potatoes, as well as rarer-than-gold herbs like basil and parsley. This in turn has enabled the paladares to be more ambitious with their menus, and some of Cuba's top homegrown chefs have come back from Europe to cook high quality cuisine for their people once more.

“There is another Cuban revolution taking place right now – in cuisine,” said Buwalda, as we hopped into her classic 1950s Buick and drove a few blocks to another teeming street market. “There seems to be a new restaurant opening up every week, and the standard is getting higher and higher.”

Buwalda moved to Cuba from her native Ireland a few years ago, after falling in love with the country during a salsa dancing holiday. Having run a restaurant for four years in Cork, her culinary expertise puts her in an excellent position to evaluate Cuba's blossoming food scene, and her blog and tours (which almost always take place in a classic car) allow her to share her enthusiasm and insider knowledge with visitors.

In addition to visiting several local markets, the tour stopped by the 5th Avenue agroponico, an urban farm in Havana's Vedado area. During what was known as Cuba's Special Period in the early 1990s – when the collapse of the Soviet Union decimated the country’s income and led to years of fierce cuts in government spending – a number of workers' collectives were formed to transform unused plots of city wasteland into farms to provide basic fruits and vegetables for the increasingly desperate population.

The urban farms started at a small scale, growing mostly greens, and not at the rate needed to supply the whole of Havana. But in many ways, the creation of these farms laid the foundation for the recent culinary revolution in Cuba.

“You could say that the agroponics kickstarted the transformation of the Cuban food scene,” said Buwalda. “They were the first places to make ingredients that weren't widely available on the state ration. And they're all run by the workers – that's my version of communism.”

This previously unavailable produce also fed into the new ambitions of restaurant chefs – ambitions that have been realised over the past few years as rules regarding private enterprise have been loosened.

Today the agroponic farm has 48 lovingly tended organic beds, growing everything from spinach to pak choi. And the private market stalls play an important role in supplying this hard-to-find produce to a wider majority of Havana residents, who did not always have the access (or the money) to shop from the farms in the same way as the restaurants.

Another short trip in the Buick brought us to the front door of Casa Miglis, a paladares turned restaurant where the home has become dwarfed by the size of the dining area – a distinct change from when paladares were restricted from being bigger than one room. Situated in a shabby housing block in Havana Centro – a mainly residential area with washing lines hung across the street and kids playing games of softball on the corner – walking inside is like being transported to another country. Sweden, in fact. Owner Michel Miglis is half-Cuban, half-Swedish, and his wonderfully surreal restaurant-bar – which opened in 2012 after almost five years of trying – reflects his roots, serving up dishes such as shrimp skagen (seafood on toast) in a modernist Scandinavian setting. It epitomises the new wave of Cuban cuisine. “I lost count of the number of times I had meetings with the government about opening this place,” he said. “I never thought it would happen.” Miglis has certainly made the most of the opportunity, with plans to extend a back room into a nightclub by early 2014. “The idea of eating out and having a few drinks in the evening might be common in Europe or America,” he said. “But it’s still really new in Cuba.” While most of the cocktails on offer are Cuban classics, such as daiquiris and mojitos, Casa Miglis stands out by being the only place in Cuba with hookah water pipes.

The next stop was Milano Lounge Club, an Italian restaurant set in a gleaming white house in the Miramar district. “An Italian restaurant might not sound very exciting to you,” said Buwalda as we walked past the pristine tables laden with bruschetta. “But good Italian [food] in Cuba is very hard to find.” Opened earlier this year by Havana-born Daymarys Camejo, who recently moved back to the city after living in Milan for nearly two decades, the restaurant's chefs make their own pasta – pasta still being almost non-existent in shops – and put the agroponic farm herbs to excellent use. The veal with tuna and capers, for example, is a favourite among the entree choices.

The last stop was another recent opening, albeit one that was a little less grand. “This is where Cubans really like to come and eat,” said Buwalda, standing next to the hole-in-the wall burger joint named 5tA, after its location on the corner of 5th and A streets. “You've got to try their speciality.” The lunchtime queue stretched around the block, but the house burger was well worth the wait: a juicy pork-and-beef patty, topped with cream cheese and strawberry jam. It is a combination that only a country in the early throes of rampant food experimentation could come up with – but one that is delicious all the same.