Yes, I admit it, I’m cheap. And that’s what attracted me to the idea of home swapping, instead of staying in a hotel or self-catering. And, yes, true to billing, our trip to Stockholm was certainly cheap. What I didn’t bargain for was that it would also be eerie – and would make us, briefly, question our place in this world.

But to begin at the beginning, I considered a few homeswap websites, and settled on Homelink, mainly because it seemed to attract people wanting to swap with homes in Britain. The homeswap experience is like internet dating, without the fear of having to meet some dodgy people off the web. I posted up photos and details of our flat, and set about the search, initially homing in on Copenhagen.

Many happy hours were spent scrolling and drooling over designer pads – but what I hadn’t banked on is that others are scrolling and drooling over you. Our first “approach” was from someone called Wanda: “Hey Helen – wanna come to Malibu?” We did not want to go to Malibu, but when a nice couple from Stockholm asked if we were up for it, we said yes. Stockholm, Copenhagen, it’s all the same isn’t it?

But then the doubts started. Friends asked how we could trust these Swedes after just a few e-mails. In the end I decided that because they had a toddler the same age as our daughter they wouldn’t have time for black-market operations.

When we got to their flat, it was not only better than we expected, but immaculately clean, devoid of any of their valuable possessions, and festooned with welcoming gifts. This sent me into a lather of politeness anxiety – were they stepping horrified into our squalor? This was exacerbated by the fact that 20 minutes into our stay we (OK she) had broken a sugar pot, pulled down a curtain and scattered a drawer of intimate-looking letters on the floor (dammit, if only I could read Swedish).

Once we had unpacked, something odd started to dawn on us. The flat was the same layout as our own. The fridge had most of the same stuff in it, the bookshelf had most of the same books. Mrs Stockholm clearly shared my fascination with natural yoghurt and strange hats, Mr Stockholm had the same musical tastes as my boyfriend, and Baby Stockholm, like her London doppelgänger, loved trucks and diggers. Experienced home swappers talk about the beauty of holidaying in a “home from home”; we hadn’t expected that to feel so literal.

Of course this has big advantages, especially with young children. We had agreed to leave everything behind for the other family to use. It was a relief to travel so light – but also, for a child, the greatest thrill is Other Kids’ Stuff. Our daughter loved the old-fashioned pram that is the norm in Sweden, and we were given great tips on places that they trundled their daughter to in it, in what amounted to a guide to living their life. Were we imagining a note of recognition in the waitress’s eyes when we inherited our hosts’ daily addiction to the freshly baked cinnamon buns at a waterside café?

At first we were amazed at how two families so similar were thrown together by fate. But it wasn’t so much of a coincidence. We were just another example of typical urban-dwelling yuppie thirtysomething nightmares, living a cliché. We imagined ourselves unique – the reverse was the case. Countless numbers of us are following the same path, in London, in Stockholm, everywhere. This was a disquieting revelation. Travel had broadened our minds – into realising how narrow ours were.

We came home to a cleaner flat, with money to spare: having paid for the cost of our Ryanair flights, and a few groceries, which, in an expensive country like Sweden, is pretty good going. But just as importantly, the holiday was convenient. And just as importantly, it was fascinating. Needless to say, we are addicted, and have set up our next match. We are just hoping it is not – quite – as good.

Need to know

Helen Rumbelow booked her house swap through Homelink (www.homelink.org.uk), which has exchange homes in 73 countries. Other organisations are Intervac (www.intervac.com), with homes in 50 countries, and Home Exchange (www.homeexchange.com) which has 15,000 listings.

Another way to book a free night is to log on to www.couchsurfing.com, a site with 366,000 users that connects people who have a spare sofa for someone to sleep on: 33,000 cities are represented worldwide. The idea is to exchange cultural experiences and to get to know a place from a local’s point of view. Guests are encouraged to buy hosts a meal at the end of their stay to say thank you.

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