Just 80 miles north of the hedonistic strip of Miami’s South Beach lies somewhere altogether more rarefied. I’m driving up an oceanside road that carves through a string of small towns such as Gulf Stream and Briny Breezes, all sitting on a long, thin strip of land separated from the mainland by the vast Lake Worth Lagoon.

I pass towering, serviced apartment blocks interspersed with elegant mansions that are embellished with columns and balconies. And, as I approach my destination, the houses become more elaborate. There are Islamic-style turrets, Italianate crests, and sculptures of lions, eagles and elephants perched on pillars that guard the gates.

Vast, precision-trimmed box hedges hide some of these residences from the road, though the ocean-front homes are more visible. Eventually, I pull into a parking space on one of the most fabulous streets in Florida: Worth Avenue in Palm Beach.

With a year-round population of just under 10,000, Palm Beach sits on its own island that’s 18 miles long, and, in some places, only 500ft wide. But what it lacks in size it makes up for in just about everything else.

It’s the Florida city with the most billionaires – there are thought to be 57 – and those incredible homes belong to chief executives, actors and rock stars. Famous residents include Rod Stewart, the late fashion icon Iris Apfel, Sylvester Stallone, and a certain orange-hued, blond-quiffed presidential hopeful. I had passed the pastel pink walls of Mar-a-Lago on my way here, though hadn’t seen a sign of Donald Trump.

So how did this tiny destination evolve to become one of the most sought-after pieces of real estate in Florida? To find out, I head to the Henry Morrison Flagler Museum (entry $26, flaglermuseum.us).

Flagler, a wealthy industrialist and co-founder of Standard Oil, was the first person to put Palm Beach on the map; as I stroll around his palatial, 55-room former home, I learn how he established the Florida East Coast Railway after falling for the warm climate when visiting from New York.

“Flager stayed further north in St Augustine, but was disillusioned with the quality of hotels on offer and the time it took to get there by rail,” explains the museum’s public affairs director, David Carson.

“He decided to look for somewhere down the coast where he could build a great hotel, and link to it with a new, more efficient railway.”

Flagler’s research led him to an unassuming patch of scrubland covered in the coconut-palms that gave the area its name; ripe for development, he described it as “a veritable paradise”.

He constructed his first hotel there, the Royal Poinciana, in 1894. At the time, it was the world’s largest wooden structure.

It no longer exists, but, by 1926, Flagler’s second, beachfront hotel, The Breakers (thebreakers.com) – a magnificent edifice designed in Italian Renaissance style – was drawing guests from Gilded Age families, including the Vanderbilts, Astors and Rockefellers, as well as banker JP Morgan and publisher William Randolph Hearst

Eventually these wealthy guests also wanted homes here, at which point up-and-coming architect Addison Mizner was the go-to for mansions which boasted his signature Mediterranean Revival style, combining influences from classical European buildings.

I head back to Worth Avenue the next day to see one of his most famous structures, during a walking tour led by local historian Rick Rose ($25, worth-avenue.com).

“Mizner had been living in the South of France but when the Second World War broke out, the social scene there ended,” explains Rose.

“A friend persuaded him to move back to the US and recreate it in Palm Beach instead.”

Mizner duly created a club on the avenue called The Everglades, which swiftly became the only place to go, hosting balls, galas and fashion shows. Anyone who was anyone wanted to be a member.

This sense of aspiration is at the heart of Apple TV+’s new comedy Palm Royale, in which Kristen Wiig’s ambitious character Maxine will do anything to befriend the high society who mingle at the fictional Palm Beach club the show is named after.

Worth Avenue was where then-up-and-coming designers established stores, after showing their wares to customers – who came to include the likes of Jackie Onassis and Judy Garland – at The Everglades. Names from Gucci to Oscar de la Renta and local Lilly Pulitzer started the trend now known as resort wear, crafting light, airy outfits that not only looked stylish but helped beat the heat.

I learn more at a fascinating fashion exhibition called Endless Summer at the Historical Society of Palm Beach County (free, pbchistory.org).

As for Mizner, having seen how well Palm Beach had developed, he decided to create somewhere similar, purchasing cheap land in a small town called Boca Raton, 25 miles south. Reportedly miffed at not having been asked to design The Breakers, he countered with a magnificent resort of his own, The Cloister Inn (now called The Boca Raton).

His punt paid off. It attracted the same crowd from Palm Beach, and while it has since expanded, the original building still stands, with its grand staircase, dark wood ceilings and old tiled floors. Today it’s only open to guests or members, creating an exclusive atmosphere not dissimilar to that of The Everglades.

I have dinner at its elegant Flamingo Grill restaurant and am offered a signature wine it has just launched under a label called, by sheer coincidence, Palmier Royale. It’s serendipitous, and sums up the high-end ethos of the area. For just a short while, I feel like I belong to a level of society I never would in real life – and, like Palm Royale’s Maxine, I see the appeal.

‘Palm Royale’ streams on Apple TV+ on 20 March

How to get there
The writer flew with Virgin Atlantic from London to Miami, returns from £399, virginatlantic.com.

Where to stay
Doubles at The Boca Raton from around £346, thebocaraton.com.  

More information
thepalmbeaches.com
visittheusa.co.uk