It was, incongruously, the ageless hipster Georgie Fame who told me about the island of Waiheke.

I was at the bar in Ronnie Scott’s, Soho, where he had just performed a set, and I paid no attention to the unassuming figure in a baseball cap who slid in next to me, until he spoke.

I had been talking about a planned trip to New Zealand, and Clive (“Georgie” disappears offstage) politely interrupted to ask me, in distinctive gravelly tones, where exactly I was going, as he had been on tour there last year. I told him I was flying into Auckland and on to Christchurch.

“Do yourself a favour,” he said, pointing a loaded glass of wine at me for emphasis. “It’s a long way down. Get out to Waiheke for a couple of days to kill the jet lag. Good lodges, excellent restaurants at the vineyards, nice people and a great Maori jazz trio who play Saturday nights.” Never having had travel advice from an R&B legend before, I decided to do just that.

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A couple of months later, within an hour and a half of landing at Auckland airport, I was walking off a boat and onto the pier at Matiatia, the terminus for Waiheke. Until the late 1980s this lovely island of green hills and rugged coves was a backwater, home to a scattering of “bach” (pronounced batch, and originating from bachelor pad) holiday homes, which were often little more than weekend shacks for Aucklanders, plus a few thousand year-rounders.

The reason it all changed was the high-speed ferry that I had arrived on. Throughout the booming 1990s, these regular fast ferries created a new class of islander: the commuter. It was suddenly possible to work in the city and still live the laid-back island lifestyle.

Money started to flow across the straits and the baches became threatened by sleek steel-and-glass structures, each costing millions of dollars. Waiheke was in danger of losing its rural, out-of-town appeal and becoming a kind of Hamptons, full of rich commuters and weekenders.

“That’s all stopped for now,” said Max, my ride from the pier, with relief in his voice. He is one of the 8,000 permanent residents who saw the escapist virtues of Waiheke being rapidly eroded. “The recession means that prices have dropped. Nobody can afford to build now.” He laughed. “Unless they own a vineyard.”

Max deposited me at the four-suite Breakfast on the Beach (00 64-9 372 2682, breakfastonthe beach.co.nz; £123pp), one of the newest lodges on the island and an impressive example of modern inside-out living, fitted with glass screens that can turn the lounge into a patio.

Keith and Marilyn Graham, the owners, once had their own bach on this beach, but, having retired, they demolished the buildings and created a very upmarket B&B. “We don’t do dinner,” says Keith. “We can’t compete with the vineyard restaurants. Instead, I give guests a ride to wherever they want to eat that evening.”

So at 7pm, Keith dropped me at The Shed, the restaurant that is part of the Te Motu vineyard (9 372 6884, temotu.co.nz), one of the 13 or so places where you can dine and sup among the vines that create Waiheke’s most famous export. The Shed is not a witty piece of self-deprecation but an accurate description of what it is. Or was: a tool shed.

It has grown organically, that is by judicious application of two-by-fours and Perspex sheeting, and has an attractive ad hoc flavour about it — service is as casual as the surroundings, so don’t go if you have a pressing engagement. The majority of the Waiheke vineyards are small enough to reflect the character of their owners, who range from ex- hippies to accountants.

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