Scandinavia consistently comes out tops in the family-friendly stakes, but is it really any healthier raising a family there than in the UK? Lucy McDonald swapped places with Danish mum of three Nina Kragh to find out

Sometimes it seems hard to be a parent in the UK. Hard to get your kid into a decent state school; hard to be a working mum; hard to be a stay-at-home mum; and hard to protect your children against the paedophile who – according to newspaper headlines – is probably living next door but one. Sometimes it makes me start to panic. Not only about my capabilities as a mum and society at large, but also how, in the face of such supposed adversity, my child could possibly grow up happy.

But is it just this country? Might bringing up children be easier somewhere else?

After the birth of my first daughter in 2006, Denmark kept cropping up. I read Oliver James's Affluenza, in which he declared the Danes the "happiest people in the world". Shortly afterwards, a Unicef report ranked Danish children's wellbeing third (just behind the Netherlands and Sweden) among industrialised countries. British children came 21st – bottom.

There were newspaper stories about Denmark's forest school nurseries, a supportive state that heavily subsidises childcare, and an education system that encourages children to be children and in which teachers are more concerned with pupils' social development and happiness than the school's advancement up a league table. It sounded like a family-friendly nirvana. So I decided to find out for myself and ended up swapping lives with Nina Kragh, a journalist from the Danish newspaper Politiken.

She was to stay in my west London house with her partner and three children and live my life, while I was to take my husband, James, and two daughters, Elizabeth, four, and Sophia, two, to stay in her Copenhagen home to see if the Scandinavian dream was a reality.

The differences in the way we live were immediately clear. Nina lives in a three-storey townhouse in the city centre, and when we arrive there are children of all ages playing unsupervised in the street, which is flanked by sandpits, a wooden playhouse and picnic tables. Here children take priority over cars.

Nina says: "The children play in the street all the time. Even my youngest, Yrsa, who is two, goes out there with her older sisters. It's common across Denmark." It sounds unbelievable, especially to a paranoid Londoner who rarely lets her own children out of sight. Two days later I have gone native and my daughters are playing outside "alone" – well kind of; I'm hovering on the doorstep.

From my vantage point I notice several blanket-covered prams left outside houses and am amazed to learn that there are sleeping babies in them. Unsupervised! Outside! Can you imagine that happening here? It did happen in New York a decade ago, when a Danish mother left her daughter outside a restaurant while she ate inside. She was arrested and narrowly escaped jail for child neglect and abandonment.

Denmark is a small country (its population is smaller than London's) with a low crime rate and a low fear of crime; perhaps this is why they legislate for the best-case scenario, where in Britain we increasingly seem to legislate for the worst.

Widely publicised cases involving British children such as the Soham murders or the death of James Bulger have helped us lose trust in one another. Although these incidences are as rare as they are shocking, they have surely influenced child-rearing in our country to a disproportionate degree.

Before I had children, I had a demanding full-time career as a television reporter. I was often away, and worked antisocial hours. It was not a job I wanted to do when I became a mother at 31, so when my maternity leave ended I went freelance. I now work two days a week and I love it because I get to spend time with my kids. In my – admittedly mainly middle-class – peer group, most mums who can afford to work part-time, freelance or have given up work altogether.

By contrast, Nina – who edits Politiken's culture section – works full-time. Most Danish mothers do. There are few housewives, even fewer househusbands, and not much of a part-time work culture. Flexi-working is common. For example, it is acceptable for parents to leave early twice a week to do the school run. And parents are allowed the first day of their child's sickness off work.

The Danes are proud of their egalitarianism, but when you scratch the surface the sexual divisions of labour are similar to here. One mother I spoke to said that although men were hands-on, it was the women "who packed the school bags, cut the toenails and organised the birthday parties".

In Denmark, childcare is heavily subsidised. Full-time nursery costs on average £300 a month. That's what I pay a week. Nannies are rare; most kids attend state-run nurseries from six months to six years, when official schooling begins.

Magda – Nina's six-year-old – attends a woodland nursery, and on the day we visit it is staffed entirely by men. In England, only 3% of early years practitioners are male. The carers are kind, warm and thoughtful but I find their gender unnerving. This has everything to do with me and nothing to do with them. When I ask if anyone minds that there are no women teachers present today, they seem perplexed and I am embarrassed by my own prejudices.

Elizabeth falls over. I turn to see one of the men pulling down her tights and checking her sore knee. Can you imagine this happening at home? Men are encouraged to be good parents at home, but are often treated as potential paedophiles outside it. With mixed messages like that, it is no wonder British men say they are confused.

Although the daycare centre is wonderful, I wouldn't want my children brought up by someone else five days a week from the age of six months to six years. But parents have little choice, because both are expected to work.

British politicians have recently lauded the Danish education system, but European-wide tests show standards have slipped in the country that once proudly claimed its state schools were the most expensive in the world. Recent research shows spending has dipped to a seven-year low. National tests from seven to 18 have been introduced to maintain standards, although, unlike in England, these are not published but solely used by teachers.

Despite these apparent setbacks, Susanne Wiborg, a London-based Danish education expert, says Denmark's system is better: "There's less stress on testing, the class sizes are smaller and the teachers look at the development of the child – emotionally, aesthetically and socially."

Britain's social divide has never been greater, but in Denmark there is almost no such thing as a low-status job. A more equal society means there is less chance of failure, so there is less pressure on children to succeed.

Unemployment is low, currently at 4.1% – compared with Britain's 7.7%. If you're unemployed there is every chance your daughter will go to the local state school alongside a lawyer's son. In Copenhagen, I meet up with an English friend who has lived there for three years. She tells a Danish joke … A woman says: "I'm nearly 30 and my biological clock is ticking and I want to have a child with my partner ... so I can look after it every other week."

Fifty-fifty shared parenting is relatively rare in Britain, but in Denmark everyone is doing it. Although in many respects the Danes exalt the family, it has one of the highest divorce rates in Europe – around 50%.

Axel Bech, the headteacher of a Copenhagen state school, says: "Parents are too liberal and put their own needs above their children's. There are lots of divorces and our children have from one to six parents. It's not uncommon to hear a child say, 'I heard you had Charles's father last year. I have him this year.'"

Although, superficially, Denmark and Britain may seem similar northern European countries, when it comes to social policy and individual familial priorities, they clearly have profoundly different mindsets.

Simplistically, Danish people and, I suppose, politics seem to place enormous importance on the pursuit of personal freedoms and gratification for both parent and child. In England, by contrast, those freedoms are not only increasingly compromised by supposedly protective legislation, but also willingly sacrificed on the altar of parental paranoia.

With that in mind, I think I would prefer my children to grow up under a more relaxed and trusting Danish regime. However, despite the unfriendly working practices and the limited state support for working parents – something that will probably worsen under the current government – I prefer the English model. I don't think I would have had the confidence to temporarily turn my back on my career in order to spend my children's most formative years with them if the prevailing orthodoxy considered such a path unusual.

I am a feminist and it is likely that my husband would have been the one to downscale his working life had I been the higher earner, but I am a mother first. Some people sneer at the perceived compromise, but for me it is the opposite. Feminism, at its philosophical heart, has always been about choices. I feel extremely lucky to have been offered this choice – and wonder whether it would have been so readily available in Denmark. Lucy McDonald

Life swap: Nina Kragh's story

It was one of those unexpected days. Deep in thought as to my next assignment, I looked up to hear my editor wonder if I'd like to swap lives with a British journalist who wanted to sample Danish family life. Apparently, international studies suggest Danish family life is the happiest in the world.

What would she be able to discover from my stressful life? Happiness? Hmmm. Perhaps. On a good day. Nonetheless, the project sounded like fun and I began corresponding with Lucy McDonald. She told me about her life in London, and about mothers who give up their careers to look after their children until they go to school. To me, that sounded like a step backwards for women, and I thought that in Denmark we had probably moved on quite a bit.

However, my stay in London raised doubts. Have we Danes really found the formula for a happy family life? Or have we just got used to life as we live it – stressed and busy? Do our children pay the price for parental happiness that no one dares to talk about?

I arrived at Lucy's home in Chiswick, west London and found that, in many ways, our lives were similar. We both have a semi-detached house in a nice area, the same books on our shelves and the same anti-nit treatment in the medicine cabinet.

But I quickly discovered the differences ran much deeper. Why were there no children in the streets – apart from those who were on their way to or from school? Where were all the sounds of a playful childhood?

In London, it was plain to me that mothers were the ones who primarily looked after the children. My husband had been on leave in Denmark for three months with Yrsa, aged two, while I went back to work. He also took care of the children while I was in London. Walking around London, my husband saw just one father during the daytime taking care of his young child. When I visited a Montessori private pre-school with my two youngest daughters, only one father delivered a child to the institution.

After parking their identical scooters inside, the children donned smocks with their names sewn on. They played with trains, colours and dolls – until it was time to learn to write and do sums.

For a mother who happily sends her daughter to an outdoor woodland kindergarten, based on hippie teaching principles from the beginning of the 1970s, it was an odd experience. In Denmark, children start school at the age of six and do not receive formal teaching until then. When I saw a four-year-old write perfectly in his exercise book and do maths, I realised how differently we view children and teaching in Denmark and England.

Around 63 languages are spoken at the Chiswick community school. That shows how big a melting pot London is compared with Copenhagen. It highlights the challenges faced by the headteacher, Alan Howson, compared with the sheltered school my eldest stepdaughter attends in our upper middle-class neighbourhood in Copenhagen.

To Manna, 10, the school uniforms isare the main proof of a major difference. My thoughts go to the Hannah Montana-inspired dress that Manna and her friends put on in the morning, and I wonder if, perhaps, a school uniform isn't actually quite a good idea. I fail to fully convince myself of the advantages, and definitely fail to explain the idea to Manna.

Another difference is the fencing all round the school and the fact that pupils can't just walk around the school – something Manna questions.

Howson says the school wants to protect pupils from "unwanted visitors". During my stay I become aware of parents' fear of paedophiles and other dangers. I come to realise that there is a different level of paranoia among British parents compared with Danish ones.

There is no reason to believe that we have figured it all out in Denmark, with a gender-equality tyranny that forces us back to work after maternity leave, but after a week in London my feeling is that there is an unreasonable pressure on working mothers in Britain. There is a constant stream of "surveys" telling them that they have fat children, drive them to school too much and don't give them enough fruit – in fact, just about all the blame for children's dysfunction is put on the mother's shoulders.

If these sorts of stories were published in Denmark, the reaction would be: what about working fathers? What are they responsible for? And men would claim: we, too, want to be responsible for our children's dysfunction!

I have never seen myself as a feminist. I am a woman who has a job she loves, at the same time as being the mother of three children I look forward to coming home to. I believe I can do both. But the thought that there is a choice, if it is financially possible, to stay at home with small children instead of having them looked after by others, is one that has taken hold.

Would I swap my existence with that of a housewife? I am not sure. But one thing I do know is that if I were a woman and mother in England, I would rapidly join the ranks of the feminists. Nina Kragh