'You eat the soup with a knife and fork," smiles Jane, my blond Swedish cousin, as I peer into a bowl of dauntingly named summer meadow soup. Blobs of orange and brown vegetable matter float in a pool of grey froth, sprinkled with what might be wood shavings. So this is cutting-edge Scandinavian cuisine. I lift half the meadow on to my fork and breathe deeply.
We're dining in Matbaren, a Michelin-starred bistro in the Grand Hotel in Stockholm. It's a dark-wood room that's lit until 10pm by the silver gleam of the midsummer sun. Around us is a buzz of smart city folk crowding the tables, ordering wooden trays of avant-garde food. The Grand is Sweden's finest hotel, the place where the Nobel prize-winners stay, across the water from the baroque façade of the Royal Palace. It's the night before I sail into the choppy waters of the Stockholm archipelago, and I'm catching a last evening of urban living.
The soup, which tastes fabulous, captures the moment – a midsummer medley of woodland flavours such as artichokes and bitter leaves, rooted in a truffle broth. Jane leans across and whispers: "Where you are going is like nothing you have ever seen." Her blue eyes sparkle. "The archipelago is so beautiful. I want to live there myself."
The cluster of islands off the coast of eastern Sweden forms the biggest archipelago in the world, with more rocks, skerries, islets and habitable chunks than Indonesia or the Canadian Arctic. Stockholm is the start of a chain of 28,945 of them, stretching 60km towards the open waters of the Baltic Sea. And, following the track of the midnight sun, it's where I'm heading in the morning.
The morning dawns clear. Outside the Grand Hotel is the ferry wharf for the islands. I climb aboard and we're off, thundering past the medieval alleys of the old town and out – to a seascape of rocky islets sprinkled with wooden cottages and pine trees. Motor boats zip past, yachts stretch their sails and swans preen on the swell.
These chalets, painted rust-red and mustard-yellow, are holiday homes for Stockholmers. Most islands have a house or two hidden among the trees, and a yacht or three moored along the granite shore. Locals spend weekends or weeks out here, from May to September, escaping the city for a simpler life.
My first stop is Grinda, a large island two hours out that's a popular spot for renting a chalet. The ferry clangs to the jetty where I am met by Lars Sunekvist, a big man with a bigger smile, who drives me in a dusty golf cart to the island's only hotel, Grinda Wardshus. We putter through rippling woods where he says there are deer and foxes. Lars shouts over the engine: "I brought up my kids on this island for two years. There were only three permanent families here. It gave them a different perspective. They didn't have 24/7 shopping, but it was peaceful. We just spent time together."
As are many families here, playing outside simple cabins or tumbling in the water. "The island is owned by Stockholm city council," says Lars, "so you can roam everywhere and the houses can be rented by anyone. It's not like other islands, which are privately owned."
He drops me at my own wooden shack behind the hotel, but I walk straight down to the island's tiny harbour. A trio of blond-haired dudes in shades are running a kayak shack, and I ask if I can hire one. They hand me a paddle and a life vest. I stammer that I haven't done this for a very long time and should I have an instructor? They look at me and at the sea. One drawls: "Well, it doesn't look like rain. You'll be OK. Here's a map."
I paddle out of the sheltered bay and along the granite shore, trying to recall the capsize routine. The waters are green and deep. I pull out of sight of people and houses. A seagull soars overhead. I stop and let the kayak drift, silent, staring at the milky sky and the rolling water. It's just me and the sea. I wonder whether my Swedish ancestors paddled or rowed around here, in the centuries before petrol engines.
In earlier times these narrow channels guarded the approaches to Stockholm, and were the haunt of sailors and smugglers. The great shipwreck on show in Stockholm, the Vasa, was on its way out here when it sank in 1628. Grinda was a major stop on the nautical route, first mentioned in 1777 for its seafarers' inn – whose ruins still lie by the ferry point.
Today's successor to that antique inn is the Grinda Wardshus. It's a gem of Arts and Crafts architecture, with steep roofs and cream walls, built in 1906 by the architect of Stockholm's Grand Hotel. I take dinner on the garden terrace, where trailing silver birches frame a view across pewter waters to island after island after island. The sun sets slowly, laying a trail of gold from white sky to grey shore.
Next morning I board a bigger ferry packed with holidaymakers heading for Sandhamn – the busiest and smartest of the islands. It's an hour further on, in the outer archipelago, but it's been a fashionable resort since the Royal Swedish Yacht Club built its headquarters here in 1897. After Grinda, its sandy shoreline of wooden villas and big yachts feels crowded. There's a delicatessen selling oysters and scarlet lobsters, and shirtless boys on yachts are flirting with languid girls in torn-off T-shirts.
I'm here to meet Anders Naslund, one of the few fishermen still active in the archipelago. Most of them left in the 1950s, when a younger generation answered the call of modern living and left the archipelago for jobs and homes in the cities. Anders, I'm told, lives in a house "behind the bakery". I search the sandy paths of the village, through a jumble of wooden villas and picket fences shaded by fruit trees. The bakery is a shack hidden by white flowers, and beside it is a path that's blocked by a weather-beaten oar. This has to be the place.
I walk down the curve of path between clouds of marguerites and poppies. There's a brown house beside green water and a yellow-haired man in blue oilskins. A knife dangles from his braces. Anders. A twinkling smile lights up a sea-creased face, and we sit by the shore and talk. He tells me of growing up on the island, when there were only seven families here, and piloting the cargo boats, and his fish trap that takes three days to build every spring, and the biggest fish he ever caught – a 22kg (48lb) salmon as tall as his shoulders.
Anders says people come from all over the world to sit in this garden and eat his fish. Then he shows me the smokery – an outdoor cupboard that creaks open to reveal blackened walls, treacly from years of smoke and fish oil. He holds up a handful of pine branches and explains that these impart the special flavour. Beside them is a tree stump with an axe buried to the haft.
I wander back to the busy harbour and lunch at the Sandhamn Yacht Hotel. Originally the Yacht Club, it's another fine Arts and Crafts building, with a spectacular restaurant overlooking the marina and lit by ships' lanterns. A plate of herring arrives, soused in vodka and sluiced with vanilla and lingonberry sauce.
Waiting for me outside are Adam Svensson, the long-haired hotel boatman who will take me to the last and remotest of my islands, and Lisa Lindskog, a student who lives there and needs a lift. We tramp down the jetty to Adam's shiny motorboat, which he guns into top speed. "I used to sail for the navy," he grins, and heels the boat hard to avoid a rock.
Twenty minutes later, a ridged island appears, dense with trees, and Adam cuts the engine as we drift slowly around an inlet into a secret anchorage. There are cabins among the pines. A jetty appears, below a tiny shop with a hand-painted sign: Haro Lius – "Haro Store". Outside are Lisa's mother Kirsten and her sisters, and we're greeted with whoops and embraces as we leap ashore.
Haro is an island way off the beaten track. There's nothing here – and nothing beyond it to the Baltic. Kirsten shows me round her shop. "We can't get fresh meat," she says, "and vegetables come by boat." But she does sell Italian olives and frozen steaks. "Now," she smiles, "let's go out in a boat."
The motor launch is skippered by her husband, Bjorn. He's a soft-spoken man in his sixties, happy to see his daughters enjoy the breeze as we whizz towards the open sea. "Forty knots!" he shouts as we bounce on the deck. Ahead of us the islands thin out and then there is emptiness. Stone-blue water meets stone-blue sky. It is the edge of the archipelago. Finally we turn back and moor beside their summer house, a pretty red cabin on a hill above the inlet. Bjorn murmurs: "I've been coming here for 65 years. As a boy I used to row from house to house selling fish. In winter it froze over, and we used to skate between the islands. I was very lucky to have this."
Below their house is a midsummer maypole, left from the festival in June. Beside the path I find a crown of leaves.
We talk until late in the silver light on a deck above the sea. Then Lisa says: "How about a sauna?" She points to an old brown hut among tall grasses. Kirsten goes to light the logs. We linger over chilled white wine, then change into our swimming costumes and brave the heat.
It is roasting. My skin seems to crisp, and then they make more steam. Sweat runs down our bodies. The girls talk of childhood summers spent out here. Then someone opens the door and we run out to the twilight, down to the creek's edge, and plunge straight in.
The waters of the Baltic close over me, black and thick and cool. I bob back up. The others are around me, laughing and joking, and around us all are ridges of pine trees, black against the never-ending sky. I lie on my back. A fish leaps close by. The archipelago surrounds me.
Stockholm’s main airport, Arlanda, is served by British Airways (0844 493 0787; ba.com) from Heathrow; Norwegian (00 47 21 49 00 15; norwegian.com) from Gatwick and Edinburgh; and SAS (0870 60 727 727; flysas.com) from Heathrow, Edinburgh and Manchester.
Ryanair (0871 246 0000; ryanair.com) flies from Stansted to Skavsta (88km south-east of the city) and Vasteras (96km east), and from Edinburgh to Skavsta.
Frequent inexpensive ferries to populated islands are run by Waxholmsbolaget (0046 8 100 222; visitskargarden.se) whose five-day boat pass costs Skr420 (£39). This entitles you to travel on any boat, any time, during its validity. Boats run year round.
Faster, more expensive, boats are run by Cinderella Batarna (00 46 8 12 00 40 00; cinderellabatarna.com), with tickets starting at Skr95 (£8.60). Boats stop 25 Nov.
Grand Hotel, Stockholm (00 468 679 3500; grandhotel.se). Doubles from Skr1,890 (£179), room only. Grinda Wardshus, Grinda (00 46 8 542 49 491; grindawardshus.se). Doubles start at Skr995 (£95) including breakfast; two-bedroom cottages cost from Skr3,000 (£286) per week.
Sandhamn Yacht Hotel, Sandhamn (00 46 8 574 504 00; sandhamn.com).
Doubles start at Skr1,495 (£142), half board.
Eating and drinking there