We walked through a gate, pushed under dripping palms — and encountered a parallel world in the midst of Old Havana. “This is the cloister of an 18th-century convent,” explained my guide, Ayleen Robainas, an architect. “It’s a very important building. And about 60 people live here.” Here, makeshift bothies had been erected amid the decaying splendour of the convent of Santa Teresa de Jesus, supporting a lively if ramshackle world where women conversed, roosters pecked and washing dried.

I was in Havana to find out how tourism is being woven into its restoration, and I could see why the adjective “crumbling” was so often used in relation to the Cuban capital. “It’s particularly bad after the hurricanes,” said Juliet Barclay. “The rain softens the stone up. Three days later, another 16th-century house falls down. And sometimes it takes its inhabitants with it.”

A brisk Englishwoman in her forties, Barclay works in Havana’s department of cultural heritage. She came to Cuba in the 1980s and met Eusebio Leal, the “Officer of the Historic City” (like a cultural mayor), the man of destiny who has taken on the task of rescuing Havana from terminal decay. Bewitched, Juliet returned to live here. “I knew I had to be involved.”

Havana is known for its architecture, and suits being slightly decrepit. It gives it a fabulous salty air — that ruinous Graham Greene glamour. Those patched-up Buicks look so cool in front of peeling walls of ancient paint. It’s picturesque. It’s also in peril. “Some people say, ‘Oh, it’s lovely and romantic,’ ” said Juliet. “But it can’t stay like that for ever.”

As the most important Caribbean city, Old Havana became a Unesco World Heritage Site in 1982. But this didn’t stop it falling down, and Leal decided that in order to attract tourists, it needed to be restored. A company, Habaguanex, was started in 1994, a kind of socialist National Trust, the idea being to glean tourism’s hard currency then filter it into further regeneration, in tandem with social and cultural programmes. A decade on, it runs hotels, bars and restaurants — even the horses and carriages.

After locating Juliet in her office in Havana’s 16th-century core, we walked to the Plaza de Armas, the city’s oldest square and a Baroque showpiece. “The colonisers wanted to make Havana as splendid as the city of Seville,” said Juliet. “It’s a little less decorated. They couldn’t do cherubs in the coral limestone.”

We lingered in the front garden of a little temple marking the site of Havana’s first Mass in 1519. It was a heady moment — perhaps because this is a semi-divine spot both for Catholics and the followers of santería, Cuba’s Afro-religion. Or maybe it was just the 38C February heat.

Juliet took me over to the shade of the Captain’s Palace, now the City Museum. This was typical of Havana’s grand palaces, begun in the 16th century: great piles with fountains in their patios, stained-glass fanlights and a mezzanine floor for the slaves. Social and business hubs, their gates have guardacantónes — ornate iron flanges put in to protect walls from rushing carriages. “These grand vehicles were to Havana as the gondola was to Venice, ” said Juliet.

There are some 144 grand houses from the 16th and 17th centuries in Old Havana and 200 from the 18th century — indeed, there are 900 important buildings in Old Havana alone, let alone the rest of the city. Leal et al have restored a handful; many remain decrepit. As I walked a few streets either side of the refurbished central area, giddy old buildings kept upright with wooden stakes loomed dangerously from pot-holed pavements.

Juliet told me how this had occurred. “The rich left Old Havana for the suburbs, and the poor moved in en masse,” she said. “The mansions became tenements and were subdivided to provide more room. Often they’d bung in an extra mezzanine floor, which gets so hot they call it the ‘barbecue’. ”

Castro’s socialism has kept them alive by neglect: demolition fortuitously was too expensive. It’s extraordinary, then, that these slums are slowly being turned into tourist hotels and shops.

We walked further into Old Havana, joined by Ayleen and Alina Ochoa, the town planner, and strolled the “golden kilometre” of Calle St Ignacio, a hot-zone of hotels, shops and building works. “We call it that because it makes enough money to fund the rest,” said Juliet, who showed me several newish Habaguanex hotels, the kind of townhouse joints where any culture-minded tourist would want to stay.

There was the Hotel Raquel, set up in 1999 for Jewish tourists and, according to Juliet, “the spark that ignited the rest”; the Hostal Valencia, an 18th-century palace with wood ceilings and balconies; the Hostal los Frailes in an old monastery, Hotel Santa Isabel, Hotel Beltrán de Santa Cruz, Palacio O’Farrill and Hotel Ambos Mundos, famed for its Ernest Hemingway connection.

Times recommends

• New York's top 10 new hotels
• A Scottish monastery retreat
• Welcome back to Rwanda