A British father living in Malmö reflects on a Scandinavian system that pays men to stay at home and keeps women in the workforce

It's around 6pm at the end of my third week of paternity leave – or pappaledigt, as it is known in Sweden – and since 5.30pm I've checked the kitchen clock every five minutes.

My daughter Eira is crying and I can't work out what she wants. I try walking her around the kitchen for what seems like the 50th time today. I thrust a maniacally smiling wooden caterpillar at her, hoping it'll placate her. I've tried whisks, pots, the colander, all objects that have fascinated in the past, but nothing works.

I peek inside her nappy, more for something to do than because I think it needs changing. I try playing her a Swedish children's song on the ukelele, but realise that's more for my own pleasure than hers. Finally I bounce her in front of the mirror in the hall, which, as always, snaps her out of it, and I stare at her happy gurgling face next to my own desperate smile.

When my wife Mia finally gets home, I hand the baby over and drop exhausted on to the sofa. I'm so tired that I'm in bed by nine, about the same time as Eira, and sleep through until 5.30am, when her coughing and crying wakes me to the next day of my six-month stint.

It has only taken a few weeks of this for me to know what the overwhelming majority of British fathers never find out.

When I thought I was being sympathetic to my wife during her child leave, I wasn't being nearly sympathetic enough. And when I thought I was being understanding, I didn't understand a thing. Here in Sweden, though, almost every father gets at least a month of baby care.

Men with prams have become such a familiar sight since shared parental leave was first introduced in 1974 (a full 41 years before parents are scheduled to get it in the UK under the government's proposals) that there's even a name – "latte pappas" – for the tribe.

At the free-of-charge, drop-in play group in Malmö that is my morning refuge, the pappas often outnumber the mammas. I'll find myself sitting cross-legged next to a taciturn Swedish engineer, a heavily tattooed biker, or another migrant – there's a computer programmer from Chennai – as our children play with the wooden blocks, rattles and drums.

One of the mammas at the group, Hanna Gronborg, who moved back here from Brixton, London, with her husband and two-year-old son two months ago, admits that she thought it odd at first. "My whole parenting experience had been played out in England, and you just don't see that many dads at playgroup or in the playground with small kids, and then I came here, and sometimes the majority are dads," she says. "It just shows how skewed my perspective had become that when I see so many dads involved in their children's lives, I am shocked."

My wife and I weren't living in Sweden when we decided to have a baby, and she allowed me to believe that six months' paternity leave was the absolute norm. In fact, the average is about three months. But one month in, I'm glad we decided to share equally, as I'm finding it rewarding in ways I hadn't anticipated.

Every latte pappa I've spoken to talks of how much closer their bond is with their children compared to how it would have been if they were a weekend and evening parent. Eira now clings to me if she's upset or tired in a way she didn't before. When friends or grandparents come around, it's me who bores them with a detailed account of her present moods, abilities and dietary preferences, so attuned have I become to each tiny passing phase in her development.

In Sweden, men's painful discovery of how exhausting it is to look after a baby is believed to aid parental harmony. "You get a whole different understanding of how it is to take care of a child, because work is nothing in comparison," says Leon, 34, a software developer I met pushing his baby daughter on one of the swings in front of a Malmö café frequented by dads who use the playground. "I don't think looking after a child for a weekend is enough. You have two days of chaos, but you don't get into the routines."

He tells me how much he misses being able to focus for more than an hour a day on anything apart from his daughter. "That was the hardest thing for me. Not having any time for myself, or being able to dig into problems that use your mind. When she falls asleep, you get to vacuum your house, tidy up, and then she's back."

I'd hoped to make a start on writing a book, but one month in I've barely written a sentence. This article was written with frustrating inefficiency in the disjointed moments when Eira was sleeping or otherwise distracted.

But we latte pappas have little to complain about. The system in Sweden is astonishingly generous. For each child, parents get to divide 480 days of leave as they see fit, with the amount set at 80% of salary, up to a maximum of 935 Swedish kronor a day (£87), for 390 days, and 180 kronor a day (£17) for the rest. Then there's a "gender equality bonus" of about £150 a month per parent, paid from the third month of the father's leave.

As my benefits are set by what's earned by the average Swedish journalist rather than by their less well-remunerated British counterparts, I may even end up financially better off.

Obviously the Swedes have to pay for it, with a top rate of tax of 56.6%, but, when the rest of their welfare state is bundled in, I'm not sure they get such a bad deal.

When I visited the UK last month I realised the extent to which people expect babies to be cared for by their mothers. Some friends, to my surprise, found my position weird. My daughter and I had lunch at a farmyard café in east London with an old university friend and her three-year-old son, and everyone from the girl on the counter to the mums that packed out the place assumed we must be a couple. It was a weekday and for them that meant no unaccompanied fathers. At a similar place in Sweden, there would be almost as many unaccompanied pappas as mammas.

The main qualities required to look after young babies – meticulous preparation and packing of baby-care equipment, a lack of squeamishness, mental resilience, even nurturing – don't now seem to me intrinsically feminine.

It's the state that pays in Sweden, so employers aren't lumbered with the direct costs. As a result, unlike the UK, where business groups have lobbied to delay the implementation of shared leave until 2015, in Sweden they actually support it.

Swedes tend to see generous shared parental leave as good for the economy, since it prevents the nation's investment in women's education and expertise from going to waste.

"There's a huge proportion of women in England who just completely disappear off the face of the earth in terms of the labour market after they've had, if not their first, then certainly their second child," Hanna Gronborg argues, contrasting this with the impact of children on her Swedish girlfriends.

"Their trajectory in terms of their jobs and their lives has remained untouched I think, whereas in England most of my friends have either gone part-time or gone freelance."