As we clambered onto the s-bahn at Hamburg Central to race across to Hamburg Altona, Alan, the friendly English chemistry researcher who had volunteered to show us the way, made a quick calculation.

“I think you’ll have at most two minutes to make it to the train, and you need to make it up to the station and up two flights of stairs.”

I rated our chances at less than 10 percent. I had booked the new sleeper launched by Sweden’s state-owned train company SJ at the very last minute (and at considerable cost) after discovering to my horror that the Danish seats-only night train I’d been planning on taking did not run on Saturdays.

My two children and I had been on the train since our Eurostar left London at 9am, and I didn’t fancy putting them through a night on the platform at Hamburg Central.

Hamburg Altona, a terminal station in the west of the city, is the departure point for SJ’s sleeper. Normally, the metro trip would only be slightly inconvenient, but when you’re racing to make a connection, it’s a nightmare. Thankfully, the sleeper will start to depart from the central station in March.

The moment we hit Altona, Alan, who lives nearby, shot off, me and my two children trailing behind as he flew up staircase after staircase.

Finally we arrived puffing at the platform, where we could see a train with an SJ logo, but the entrance to the platform was blocked. Had we missed it? “Do you have a ticket?” asked the guard, wearing a warm SJ jacket, and when I said yes gestured to the long line of people snaking right out to the station door.

I don’t think I’ve ever been more grateful for a system failure. It turned out SJ had somehow lost access to the records of who was supposed to be on the train, or where they were supposed to sleep, and were having to work out the sleeping arrangements manually, one passenger at a time.

Alan, a researcher at Hamburg’s Max Planck Institute, wished us goodbye and we joined the back of the queue, where we met a Swedish woman who’d come all the way from Italy with her red setter, a journey she said she’d been doing quite regularly ever since the sleeper service was launched in September.

Annoyingly, she told me that it was possible to get a reduced price on the sleeper if you have an Interrail card (as we did). When I checked, you could get a couchette from Hamburg to Stockholm for about 385 kronor, about a third of the price we paid. I went back to the guard and asked if there was any chance of getting our money back, at which point he erupted in mocking laughter.

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Half an hour later, at about half past ten, we finally got our seats. The woman who’d come from Italy was turned back, however, as she hadn’t booked a bed in a special dog compartment for her red setter.

We trundled up to the train, finding a young couple and a man with a Middle-Eastern background already in bed with their sheets laid out.

“It’s got beds! I’ve never been on a train with beds before!” Finn exclaimed as he sawn the couchette compartment. Unfortunately there were only two beds for us. The Thai-Swedish SJ guard disappeared into her cabin when we pointed this out, and after a short phone call came back and told the man with a Middle-Eastern background that he had to move to make space for us.

“I hope that wasn’t some kind of discrimination,” I said to the young couple after he’d gone. It was probably because he was travelling alone, however, and we later discovered that he’d been upgraded to a luxury two-person sleeper cabin, which assuaged my guilty conscience. In a further sign of the guards’ ability to improvise, when I bumped into the woman with the red setter while brushing my teeth, she said they’d also managed to accommodate her.

The couchette cars are refurbished, with free water, and USB ports for recharging your various devices. They are old, but they’re comfortable enough and Eira and Finn were both fast asleep within minutes of the train rolling out of the Hamburg.

I had just about drifted off by the time I was woken by border police at the Danish border at around midnight, sleepily reaching down from the top couchette to show them our passports.

My hope was that departing more than an hour late would delay our arrival in Malmö, which was scheduled for just before 4am, but unfortunately, the train normally travels more slowly than it needs to to allow passengers a proper night sleep, so it easily made up the lost hour.

At about quarter to four I got a friendly knock on the door, and shook the children awake in time to see the lights of Malmö’s Turning Torso tower as we crossed the Öresund Bridge.

For the remaining five or ten minutes, Eira and Finn excited pointed out “Swedish” out-of-town shopping centres until the train arrived at a completely deserted Malmö station, from where we took a taxi home.

How to get an interrail discount on the Hamburg Stockholm sleeper

On the sök resa or “search journey” page on SJ’s website, you need to click on the drop-down menu next to resenärer or “traveller”, then, when you see your name, click on ändra or “change”. Then click on another drop-down menu on välj ett kort or “choose a card”, at which point you can press Interrail and fill in your Interrail card number. You can find a guide on how to do it here on SJ’s website.