The new Interactive Rum Experience at Vinopolis, the huge wine and spirits warehouse at Borough Market, grandly claims to be the only place outside the Caribbean where you can walk through a sugar plantation or wander around a traditional rum distillery. That might be overstating the level of “interaction” on offer, but the fact it has given over space to the spirit is a sign of how far it has come since its days as an all-purpose cosh with which to govern the sea-faring classes.

According to drinks expert Dave Broom, rum is the fastest-growing spirit category in Europe, largely at the expense of whisky, and this is almost entirely attributable to superior quality, aged “sipping” rums. “The old days of Captain Morgan British blended rums are in steady decline,” he says, “and white rum, dominated by Bacardi, is flat, but even pubs like Wetherspoons, which used to just have a light and a dark rum, have a wide range. We’re starting to see aged rum appearing on the shelves of Waitrose and Tesco.”

He believes we are at similar stage as whisky was about 20 years ago, when consumers started experimenting with single malts. “Drinkers are beginning to understand the diversity,” he says. “Rum ticks all the right boxes: it has heritage, provenance, it’s hand-crafted, and each is part and parcel of an island or country’s culture. Barbados rums are the balanced, quiet diplomats; Jamaicans are big and punchy; Guyanese have a deep, mellow sweetness.”

It also makes you smile a lot, as I discovered when Broom led me through a tasting of 12 marques. “There’s something sunny about the aromas of sugar and tropical fruits,” he says. “It’s golden in colour, refreshing to look at – it makes you happy.”

There’s Angostura 1919, now based in Trinidad, but closer to Venezuela in temperament, a delicate drink with less overt aromatics. Appleton Estate from Jamaica has an intense, pineappley aroma and rich body. “It’s the Islay of the Caribbean,” says Broom, “a love-it-or-hate-it rum, and the one anyone could pick out in a blind tasting.” Chairman Reserve from St Lucia has a rich, soft, muscovado flavour and notes of overripe banana, while Barcelo Imperial from the Dominican Republic is more butterscotch. At the top end there is Doorly’s XO from Barbados, a smooth raisiny rum aged in oloroso sherry barrels.

The vast majority of rum is distilled from molasses, a by-product of the sugar industry, but because the French got their sugar from sugar beet in Europe, their former colonies such as Guadeloupe or Martinique made rum from sugar cane juice. The result, seen for example in Barbancourt Reserve 8 Year Old from Haiti, is more vegetal in character, with a floral spiciness that makes it a kissing cousin of Armagnac.

Ian Burrell, self-styled rum ambassador and owner of Cottons “rhum shack” in Camden, has 280 rums behind the bar – “and that’s only because we’ve run out of space”. He believes we are a nation of natural rum drinkers, not just because of our long association through the Navy (and more shamefully, the slave trade). “We are a ready market. We like that woody style of drink because we are whisky and brandy drinkers,” he says. “There’s a lot of goodwill towards rum. Now the consumer needs guidance about understanding how diverse it can be.”

The one he likes to start doubters on is El Dorado 15 Year Old from Guyana. “They are pleasantly surprised; it’s always the same expression you hear – ‘That’s not rum!’ And I know I’ve got them because they are discovering what true rum is about – lots of flavour, lots of complexity, lots of character.”

The Rum Experience is part of the Spirit of Vinopolis tour, which costs £27.50 including all wine, whisky, rum and beer tastings (www.vinopolis.co.uk)

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