Whenever Frank Sinatra wanted to get his neighbourhood cronies round for some late-night revelry he would, so the story goes, hoist a Jack Daniel’s flag over his Palm Springs mansion. Bourbon was his signature drink. He loved it so much they even buried him with a bottle of Jack tucked inside his pocket.

Sinatra’s heyday – when few men were seen without a stiff drink in hand – is back in fashion, and not just stateside. We’re lapping it up here in the UK too, buoyed by shamelessly boozy scenes in popular American TV dramas such as Mad Men and Boardwalk Empire. One of the consequences has been a renaissance in whisky.

Twentysomethings and thirtysomethings – whom the marketing types refer to as the “millennials” – are shunning formerly trendy brands of vodka in favour of old-school brown spirits. And American whiskies are driving it. “It’s about popular culture,” says John Hayes, managing director of Jack Daniel’s.

“What you’re seeing in the UK is a renaissance in classic American cocktails such as the Manhattan and the Old Fashioned,” he says.

This bourbon boom is not just bad news for vodka, though. Scotch whisky is getting squeezed too. Scotch does not lend itself to cocktails in the same way as some of the new, sweet-tasting bourbons, such as Jack Daniel’s Tennessee Honey, which now sells some million cases a year worldwide.

Four years ago it didn’t even exist. And now scotch’s biggest brands, such as Famous Grouse, Bell’s and Teacher’s, are starting to look staid by comparison. “Scotch has been on the market for so long that it sometimes has an old, stodgy perception. They [the scotch brands] have to be worried,” says Hayes.

Following a decade of fast growth, scotch exports were down 11% in the first half of this year, according to the Scotch Whisky Association.

The scotch industry is not nearly as worried as it should be, says Spiros Malandrakis, an analyst at research firm Euromonitor. “Bourbon, Irish and Japanese whiskies are being much more innovative,” he says.

Hayes is not alone in believing that scotch is out of touch. The Whisky Bible 2015 last month selected a Japanese single malt (the Yamazaki Single Malt Sherry Cask 2013) as the best whisky in the world.

American bourbons came second and third, while scotch failed to make even the top five – the first time this has happened in the guide’s 15-year history.

It is a wake-up call for the industry, but the bigger problem is how to win over new, younger consumers.

For a long time, scotch brands did not even bother marketing to people under 40 (at least not in the west). Scotch is a taste, the purists would argue, that you acquire later in life.

The scotch industry is now keen to change that narrative. “We need to be more in popular culture, with cool dudes,” says David Gates, drinks company Diageo’s global director of premium core brands.

His company has already signed up Mad Men star Christina Hendricks (who plays the advertising agency’s office secretary, Joan) as a brand ambassador for Johnnie Walker. Its latest gambit is to team up with David Beckham – oddly, given he is hardly a whisky drinker in the Sinatra mould – for the launch of Haig Club Single Grain Scotch. This is a brand targeted at young people who normally eschew scotch. But isn’t Beckham a bit of a safe choice? Given that he will turn 40 next year, isn’t he a bit long in the tooth to be wooing trendsetting millennials? Gates thinks not. “He is incredibly charismatic, a real star icon and bit of a game changer,” he says.

Only time will tell. There is an argument, though, that the Scotch industry needs to come up with more original marketing ideas and connect better with consumers who often feel intimidated or, worse still, bored by scotch.

The stakes are high. For more than a decade, the emerging markets have been a haven for the scotch industry. A growing, cash-rich middle class in China, Brazil and Russia couldn’t drink it fast enough. But demand has slowed dramatically over the past 18 months as economies have cooled.

Diageo’s Gates is sanguine, labelling the slowdown in the emerging markets as a blip. “You’ve got to hold your nerve,” he says.

Scotch will have to hold its nerve in western markets, too. Surging demand for American whiskies has taken the industry by surprise, says Hayes. “No one saw it coming five years ago, but there’s now a lot of pressure to keep it up.”

Stiff drinks all round, then. Sinatra, for one, would certainly approve of that.