Watching my two children struggle along the platform like geriatric tortoises under their new backpacks, I had a moment of doubt. It was 5am on a dull, Monday in London and we were about to embark on a journey that would take us, by train, all the way to Stockholm.

With the help of the Man in Seat 61 website, I worked out that a Global Interrail pass was the best way for our crew (my husband, me and our 11- and nine-year-old daughters) to get there. The pass covers most continental trains, is extremely flexible and – best of all – free for children under 12 accompanied by an adult. I also booked our hotels and a cabin on the Stockholm archipelago.

We arrived in Brussels on the Eurostar in time for breakfast and, after dropping our luggage at the BXLroom Guesthouse (a converted factory in the Stalingrad area; studio €150 a night), it was time for waffles from one of the many nearby street stalls – where a simple sugar waffle costs €1.

Brussels’ Royal Arcade. Photograph: Getty Images

We took in the Royal Arcade, lined with chocolate shops, the Grand Place, the Manneken Pis … and then moved swiftly on to the wonderful Choco-Story, the city’s chocolate museum (adult €9.50, 6-11 €6.50, under 6 free). The next morning we returned to Brussels Midi station to catch the train to Hamburg via Cologne. Two hours later, having had a brätwurst lunch at Cologne’s central station, we took the ICE train to Hamburg.

The pink-chandeliered lobby of the Reichshof Hamburg hotel (junior suite €155) welcomed us like a vision from The Grand Budapest Hotel, with the bonus of a gin cafe over the road. We walked around Alster Lake, one of the city’s two manmade lakes, which was busy on a summer’s evening with dinghies and rowing crews. The children had hamburgers in Hamburg on their minds, though, so we headed to Otto’s.

Hamburg city centre. Photograph: Getty Images

A long day of travel meant another morning railway station departure. This time the 9.30am to Copenhagen, via Puttgarden – where the train was loaded on to a hybrid ferry for a 50-minute trip across a narrow sound to Denmark. Once in Copenhagen, our gang boarded the high-speed X2000, crossed the Øresund bridge (made famous by TV series The Bridge) and, five hours later, we were at Stockholm’s Scandic 53 (superior room £160) – and ready for a good night’s sleep.

As much as I wanted to linger over Stockholm’s scandi-design, we needed to get to Strömkajen, one of the city’s two ferry ports, where a boat would take us to Hästholmen, our island home for eight days.

As Stockholm fell away, the scenery became one of rocky islands covered with pine forests. Sweden had long been a fairytale destination for me and now, sitting out on the sunny deck, gazing at red, Pippi Longstocking-esque houses that peeped out over wooden jetties, I had the sense of a dream coming true.

A boat en route to Vaxholm. Photograph: Getty Images

After an hour the boat docked at Vaxholm, the capital of the archipelago. Most passengers disembarked here, to lunch at the famous Waxholms Hotell or visit the Vaxholm fortress, a granite mass of battlements. Then the ferry was off again; the remaining passengers loaded with food and crates of beer and wine.

There are around 30,000 islands, in the Stockholm archipelago: some just rocky outcrops nested by sea birds, others, such as Vaxholm and Möja, are thriving communities. The majority, though, provide weekend and summer homes – buzzing with motor boats and hot tubs until mid-October when, it goes quiet and dark.

Finding a rental house on the archipelago from the UK wasn’t easy: there are so many islands and, to me, online information felt limited. We used Airbnb, where the houses ranged from summer palaces with their own jetties, saunas, boats and beaches, to rustic shacks that looked charming but offered little more than four wooden walls, a bed and an outdoor, composting toilet. There was, it seemed, something for everyone.

Holiday homes on Hästholmen (also known as Stegesund-Hästholmen). Photograph: Christophe Boisvieux/Getty Images

The islands are divided into the inner, middle and outer archipelago. The inner ones are clustered around Vaxholm, where we were, and are essentially Stockholm’s version of England’s home counties; while the middle is akin to the Lake District; and the outer, more like the Scottish Highlands.

Some islands, such as Skarpö, Rindö and, further south, Lidingö, are linked to the mainland by road bridges (and the road ferry). Others are car-free and reachable only by ferry or a small boat. Some of the islands, like Hästholmen, are privately owned, usually by a small consortium, while others, including Finnhamn and Grinda, are owned and maintained by The Archipelago Foundation – these are usually nature reserves. Our criteria was car-free but not too remote, accessible by public ferry and a house (with indoor plumbing) that fitted the picture I had in my head of the perfect Swedish cabin.

Arriving at one of the ferry stops on Vikingsborg Brygga, we were met by our host, Carl. We followed him up to the house along a dirt track and through a coniferous forest, bouncing gently on the springy moss underfoot and breathing in the pine-scented air.

From the moment we set foot in the cabin (sleeps four, around £765 a week in summer), we knew we had lucked out. On a rocky outcrop overlooking the sea, in a glade between the trees, this simple pine building is attached to the main house by a large wooden deck. It has two bedrooms, a bathroom, small kitchen and a living room – all decorated with homely furniture and has masses of clever, Ikea-style storage.

The writer and family’s Airbnb rental on Hästholmen

Unpacking had to wait as we had two children desperate to leap into the water. It was a five-minute walk to a wooden jetty from which we could dive into the Baltic. We took the plunge …

The water was clear, cold and less salty than we’d expected due to the fresh water coming from hundreds of rivers. Being so well-oxygenated, the water is also dense with weed. I’m an experienced wild swimmer but even I took a while to get comfortable with the aquatic undergrowth. There were also some strong currents, despite there being no tide; however, as long as you respect them and keep an eye on the shore, there’s little to be scared of here.

View from the cabin

Flying in the face of expectations, perhaps, there wasn’t a sauna with the cabin but there was a small bathing hut, and that’s where we warmed up, post-swim, with coffee and cinnamon buns.

The trip turned out to be one of the healthiest we’ve ever taken. Alcohol was expensive and difficult to buy, so apart from a few canned G&Ts I had carted from the UK, we were booze-free. Every morning, I ran the 5km of tracks through the forest but although there were about 50 houses on the island, I usually only saw a red squirrel or sleepy spider.

Breakfast meant porridge – Swedish supermarkets carry the widest range of oats I’ve ever seen – after which, on the first morning, Carl motor-boated us over to the Skärgårdens Kanotcenter, based on Resarö, a well-heeled, commuter island.

Kayaks rented from Skärgårdens Kanotcenter on Resarö island. Photograph: Cat Muir

It had been easy to book our two kayaks online and as we headed out to explore places only accessible by boat, we agreed this had been an excellent choice. We glided through the wind-ruffled waters to the Bogesund nature reserve, with its beavers and huge white eagles soaring overhead. We swam in small coves with tiny fish swarming around our feet, hiked through wildflower meadows and ate hotdogs and baked apples, cooked in designated firepits on beaches across the islands.

The days were long – the sun didn’t set until 10pm – so we had time to take a trip out to Finnhamn, an island in the middle archipelago; to eat giant raspberry and liquorice gelatos; to host our own kraftskiva, a crayfish party, singing Lily the Pink because we didn’t know the words to the traditional Swedish songs. Without us noticing, the demand for phones and devices died away, leaving just the sound of the front door slamming as the girls headed out into the forest to pick blueberries, the gentle slap of paddles on the water and the splash of happy people wild swimming.

• See our Interrailing guide to prices, passes and planning to work out which of the many passes works best for your trip. The Ferry from Stockholm to Hästholmen operated by Waxholmsbolaget, adult return from £8, 7-19s from £6

Looking for a holiday with a difference? Browse Guardian Holidays to see a range of fantastic trips