It wasn’t until a year ago that, at the bottom of a box of Eastman Kodaks, I discovered a stash of silent 8-mm film taken by my grandfather during their halcyon holidays in Bermuda. Vignettes of my grandmother bicycling past low-shuttered shops on Front Street and hunting for coins cast from shipwrecks in the coves of Horseshoe Bay fade into clusters of bay grape and mangrove, cocktails on terraces that zigzag across coral rock cliffs, and yellow-and-white-striped umbrellas that look almost toy-like from above. The footage is from the 1950s, but it may as well have been taken yesterday.

Returning to the Coral Beach Club last May, I found the familiar pink-and-green upholstery and chinoiserie of the clubhouse, the same colorful curtains and walls painted to look like wallpaper, even the same old Amazon parrot, Alonso (named after the king in The Tempest, which is believed to have been set on the island), that used to squawk at me when I was a kid. The yellow-and-white-striped umbrellas still line empty stretches of coral sand, the pink-and-white Frozen Hut still serves rum swizzles, and you still have to wear white on the tennis courts and dress for dinner. (The island’s bizarre and distinctive dress code—blazers and ties on top, Bermuda shorts and knee socks below—also remains firmly in place.)

The Dark ’n’ Stormy was invented on the island by Gosling Brothers Ltd.

Yes, this 21-mile oasis on the same latitude as Shanghai and Charleston (and just a two-and-a-half-hour flight from New York)—discovered by Juan de Bermúdez, a Spaniard, but under British rule since 1612—is a time warp of English gentility that has long seemed impervious to change. Men, who could either be just off the links of the Mid-Ocean Club or heading into the office, stroll through the narrow streets of Hamilton, the capital, wearing pastel shorts and knee-high socks. Along Front Street are rows of colorful little stores—from the Irish Linen Shop, with its bright-yellow wooden shutters, to the sky-blue headquarters of Gosling Brothers Ltd., the rum manufacturer that invented the Dark ’n’ Stormy. The English Sports Shop sells kaleidoscopic stacks of madras shirts, neckties, and—of course—Bermuda shorts and knee socks in shades as bright as the island itself. Century-old emporiums still bear their founding families’ names—there’s A. S. Cooper & Sons, Bluck’s, and Astwood Dickinson—but my favorite one of all, Trimingham’s, is now gone. Established in 1842, the storied orange department store became a Bermuda National Trust bank in 2005.

The loss of Trimingham’s isn’t the only sign of the change that seems to be afoot: In 2012, the Fairmont Hamilton Princess, an eye-catching pink palace that opened in 1885, was sold and is undergoing a $90 million renovation, two-thirds of which will be completed this spring. The first ripples of change at the Princess came last summer: Additions include an infinity pool, a handful of Andy Warhols and Damien Hirsts in the lobby, an open-air restaurant, a 60-berth marina, and a nautical-themed pop-up restaurant from chef Marcus Samuelsson, as well as a permanent Samuelsson restaurant, opening in May. This all stands in sharp contrast to the hotel’s still-regal lobby and opulent, columned Gold Room.