Be prepared to expect the unexpected in Cuba, we’d been told. And with its less well-known Jewish heritage behind the brightly coloured façade, Havana certainly didn’t disappoint.

A dignified yet dilapidated city trapped in a time warp, it boasts an extraordinary mix of narrow cobbled streets and grandiose squares, unsmiling blocks of Soviet-built council flats plonked between run-down homes with crumbling facades.

Here there are virtually no advertisements except for a handful of political billboards, music streams out from open windows and the roads are filled primarily with 1950s and 1960s vintage American cars — with our guide proudly informing us that Cuban mechanics are the best in the world!

And in a quiet residential neighbourhood in Vedado, perhaps the most interesting district apart from historic Old Havana, sits El Patronato, the city’s Jewish Community Centre.

Next door, a dozen marble steps lead to the Conservative Beth Shalom synagogue, the biggest shul in Cuba, topped with a high arch and large Magen David.

Before the revolution in 1959, there were over 15,000 Jews in Cuba. Around 90 per cent left soon after, many middle-class merchants or professionals seeking a more congenial life in America. An added spur came when atheism was declared Cuba’s national religion.

Today, the vast majority of the remaining 1,400 Jews live in Havana, a city of two million inhabitants. Despite this exodus — and Fidel Castro’s decision to break off diplomatic relations with Israel in 1973 — there has rarely been any antisemitism experienced by Cuban Jews.

Orthodox services are still held daily at the Adath Israel shul, which began life when Ashkenazi immigrants from Eastern Europe started to arrive in the 1920s to work in the garment industry, followed by refugees from the Nazis.

Nowadays the 300-strong congregation is equally divided between Ashkenazim and Sephardim. The shul proudly states that its doors have never closed and visitors are always welcome, especially for the Friday night Kabbalat Shabbat service, while it also provides a free breakfast for the often impoverished pensioners who remain.

The tranquil façade and atmospheric tree-lined streets of Vedado also house some of the country’s hottest jazz clubs, especially around La Rampa, not to mention the famed Coppelia ice-cream parlour which serves over 16,000 litres of ice cream every day.

Cruising around in a classic 1953 Plymouth convertible with our state-employed official guide, it’s simple to tailor an afternoon excursion around any particular interest.

But while the avenues with their beautiful architecture can be a welcome respite after bustling Old Havana, it’s in la Habana Vieja that you’ll find the sights which tempt most tourists, a short drive back along the famous five mile Malecon seawall.

It’s easy to explore on foot too, with time for a mojito along the way. After enjoying the spectacular views from the rooftop terrace of the swish Parque hotel with ours, we set off to wander from the Parque Central plaza.

In the centre of the square stands a marble statue of José Martí, the revolutionary poet and journalist who died in 1895 fighting for Cuba’s independence, while behind the statue you can spot the Hotel Inglaterra, the oldest hotel in Cuba where a young military reporter named Winston Churchill stayed in 1895 during the Spanish–Cuban war.

And next door stands the magnificent Gran Teatro de la Habana — the Grand Theatre of Havana — dating from 1838 and home to the renowned Cuban National Ballet.

The impressive El Capitolio, or National Capitol Building, which now houses the Cuban Academy of Sciences is closed for renovations until 2019, but it’s a splendid sight. The seat of government until the revolution, inside its treasures include the gigantic statue La Estatua de la República.

Then onwards towards the sea. A gaudy frontage of yellows, pinks and blues on the tree-lined Paseo del Prado marks the striking Hotel Sevilla, Al Capone’s haunt in the 1930s.

Or stroll the narrow streets and alleys; the most popular is the pedestrianised Calle Obispo, a bustling narrow thoroughfare jam-packed with gift shops, bars, paladares — private rather than state-run restaurants — and street vendors.

Whilst smokers might be tempted to buy from one of the women in white sitting on the pavement who always keep cigars between their lips, aficionados would do better to stock up after watching the cigars being hand-rolled at the city’s Partagas factory.

Obispo spills out onto the Plaza de Armas, a square lush with overgrown tropical vegetation as well as a beautiful ceiba tree where, on November 16, 1519, the town of San Cristobal de la Habana was founded.

Revered by many Cubans, there is a popular tradition of making wishes for prosperity on the anniversary, while making three circles around the tree, touching or even kissing it — a Santeria ritual derived from Catholic and African beliefs.

As evening arrives, the favourite place for habaneros to promenade is along the iconic Malecon esplanade itself — with the Hotel Nacional de Cuba summing up Havana’s eventful history.

This once swanky resort for Americans in the 1930s fell under control by the Mafia, hosting the Havana Conference mob summit run by Meyer Lansky and Lucky Luciano. Abandoned after Fidel Castro closed the casino, it fell into disrepair before being restored to its days of five-star luxury when Cuba reopened to tourists.

Whatever you expect from a trip to Cuba, there are always more surprises in store in this fascinating country.