It was a crisis of iceberg proportions. There we were, Jan and I, sailing along in our relationship like Leonardo DiCaprio and Kate Winslet on the Titanic’s bow, when kerrunch — our wedding anniversary loomed out of nowhere. And I’d forgotten about it.

Then kerrang! I forgot her birthday, too. And kapow! The emergency present I belatedly bought proved utterly unsuitable. I could tell by the look on her face that apologies would be like rearranging deckchairs.

A certain froideur descended over the kitchen table. Nothing but Frosties for breakfast, lunch and dinner from now on for me. Solitary confinement with no exercise rights. Conjugal visits? No chance. To recover from this jam, I needed something special and I needed it fast. There was only one solution: a long weekend away with lashings of luxury and no children. But where to go that was unusual and not too distant? Budapest? Too urban. Morocco? We’d been there. Bognor? She might not see the funny side ...

Why don’t you go to Hell, suggested a friend. So, one morning I casually tossed into the non-conversation over the Frosties: “Why don’t we go to Hell?” “That’s just silly,” she replied sternly.

“Exactly,” I said. “Scilly, isles of. Hell Bay, part of. How about Friday?” So we went.

In normal circumstances I would never have considered going to the Scilly isles, which sound like a poor man’s Seychelles. To me they conjured up images of Harold Wilson — the former prime minister who had a holiday cottage there — on the beach, exposing pallid knees while puffing a pipe. A ghastly echo of the 1960s.

But I had been assured the islands, some 30 miles southwest of Cornwall, possess a certain magic — which became apparent from the outset.

The Scillies are one of the few destinations within Britain that retain the romance of travel. To get there you have to take either a steamer or a helicopter from Cornwall, or fly in from further afield on a tiny Twin Otter.

This is a 17-seat propeller plane, with no trolley dollies doling out free drinks because a) you can’t stand up inside and b) there’s no loo. It’s the sort of plane on which you expect to see Indiana Jones hanging from the wing strut as he battles to get back to the controls — all of which makes for an atmospheric start.

The Scillies’ airport is on the island of St Mary’s, which is the largest of the group and, to my mind, the least enticing. It is big enough to have roads, banks, shops and other intrusions of civilisation, but not lively enough to hold the attention of urban socialites.

Instead, scoot across St Mary’s to the main dock and onto one of the launches that ply between the islands. We were heading for Bryher, the smallest inhabited island, and as soon as our jetboat surged out to sea the otherworldliness of the Scillies hove into view.

On all sides the ocean stretches to the horizon, a blue-grey expanse of freedom. All there is to anchor your location is the archipelago of hilly islands floating there like driftwood. Visions of Atlantis swam into my mind, which isn’t quite as barmy as it sounds. In fact, some people say the Scillies were part of a mythical lost empire, known as the Kingdom of Lyonesse. What is true is that these outcrops, though stuck out in the ocean, have a history of settlement going back to Roman times and beyond. Yet at the same time they have resisted the invasion of modernity. I found it an alluring combination, and Bryher exemplifies it.

The island, roughly a mile and a half long and half a mile wide, has two jetties, a handful of driveable tracks and a smattering of habitation.

“So where’s the luxury bit?” asked Jan.

“Down there,” I said, pointing at some old cottages and a converted cowshed on the western shore.

The Hell Bay Hotel, our destination, is the most deceptive converted cowshed I’ve ever visited. Its exterior has been kept low-key to avoid intruding on the landscape, while its interior is a haven of modern art and design. Outside, there is wilderness; inside, you retreat to designer plumbing, three-course dinners and, in our room at least, a bed so large you had to send out search parties in the night.

But what do you do, outside the hotel, on such small islands? You can watch the locals racing “gigs”, the old-style rowing boats that used to venture out into storms to rescue shipwrecked sailors. You can visit the delightfully informal Abbey Gardens of Tresco, the neighbouring island. You can take boat trips to watch seals and marvel at the reefs.

For all these activities, of course, the locals take your money with a smile — and you have no option but to pay, otherwise you are marooned. At such moments, some might find the perpetual carefree niceness of the locals a tad irritating.

But what I enjoyed most came free: it was just listening. To the sound of surf roaring into Hell Bay and seething back over the rocks. To the silence of soft, sandy beaches. To the whipping of the wind atop Badplace Hill. You realise that wherever you are on the smaller islands, there is barely a car, no rumble of trains or drone of planes, no pounding music or wailing siren. No yobs, no panic — no commotion of any sort. Just a serenity rare in southern Britain.

True, high season can be, as one local described it, “bedlam”. But I suspect a Scillonian’s bedlam is a Londoner’s ordinary day out. A mere 2,100 people live on the islands and there are only 2,500 beds for tourists. Even with day-trippers, there are unlikely to be more than 5,000 visitors (which is just a third of what the Eden Project in Cornwall sees some days).

I suppose this combination of all mod cons right next to ocean wilderness is what gives this modern Atlantis its appeal as an escape from urban stress. Some people we met said they return again and again; others spend weeks at a time here. To me, its charm seemed more suited to a short break.

On our last afternoon we walked around the whole of Bryher again, up past the skull-and-crossbones flag someone had stuck on Hangman’s Rock and over to Hell Bay. Several ships have been wrecked here, driven into the jaws of the bay by Atlantic storms.

On the hilltop path, one well-timed shove by a neglected lover would leave you well and truly splintered. But the weekend’s mission was accomplished: we stood there happily, gazing out over a peaceful swell to the horizon. And there wasn’t an iceberg in sight.

Getting there: direct flights to St Mary’s are operated by Isles of Scilly Travel (0845 710 5555, www.ios-travel.co.uk). Return fares cost £115 from Land’s End, £130 from Newquay, £210 from Exeter, £260 from Bristol and £275 from Southampton. The same company operates the ferry, which crosses between Penzance and St Mary’s in 2hr 40min and costs £85 return. British International (01736 363871, www.islesofscillyhelicopter.com) operates 20-minute helicopter flights from Penzance both to St Mary’s and Tresco, daily except Sunday, at £125 return.

The hotel: Hell Bay (01720 422947, www.hellbay.co.uk) has late deals between August 20 and September 4 from £100pp, including taxi and boat transfers from St Mary’s, breakfast and three-course table d’hôte dinner. Its regular rates start at £150pp in September.

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