Now, 9pm, 10pm maybe. It is midsummer and the sun is still up, gilding the brightly painted 17th-century buildings that line the waterfront. Once the buildings around this  slot of water housed little more than bars for sailors, straggling ashore unsteadily, staggering out hours later, even more unsteadily, to their boats – if they could find them.

This evening the place is packed with everything but seamen: tourists, young people, locals perhaps, and the accents of a dozen or more languages mix with the creak of boats on their mooring ropes and the clink of glasses. An organ-grinder complete with fake monkey makes his way around tables and stretched legs, careful not to upset frothy beers set down on the pavement by those not eating, the ones just sitting on the harbour wall. His music, when he can find a space to set up, is largely lost in the jumble of talk and clattering cutlery and competing rhythms from nearby restaurants.

Suddenly there is a rise in the noise, a rowdy German drinking song, shouts and dares and a man dives into the water. Stark naked. A jostling on the wharf, and two more follow, a fourth, and several more, white and wriggling in the dark water. They swim to the other side, haul themselves out and saunter back, mindless of the crowd.

This is Denmark. This is Copenhagen – of course!

Nowhere else in Europe, it seems, is English so perfectly spoken. Either the Danes are born linguists – and you start to believe it when you hear the canal-boat guides switching effortlessly from flawless German to English to Italian to French – or it is the force of necessity. Several times in our visit, people say: 'Denmark is such a small country. We have only five million people! How can we expect anyone to learn Danish?'

Yet there is an surprise inflection sometimes.

'Of course!' says the hotel receptionist when you ask a favour, and while her smile says 'you're welcome', there is an emphasis. In any other country, this might signal an underlying insolence. But this is Denmark, and these are the people who had enough political cunning to stay out of the last world war. These are the people who have made a lifestyle out of spoiling themselves rotten. These are the people of hygge and happiness. And, no, hygge is not the latest brew from Carlsberg. It's something a good deal more potent.

Hygge has no English equivalent. Think 'hug' though and you start to get its drift; think self-pampering, and you are getting close. Danes practice hygge when they light candles to fight gloom during their longish winters; they hygge by picnicking when the weather smiles and spending time with friends when it doesn't. Hygge is special. Hygge is uniquely Danish.

Just a few million people inhabit this water-bordered country of scattered jigsaw bits called Denmark. Pushed together the area would be slightly larger than The Netherlands and a little smaller than Estonia. But because it is so dispersed, you need days to explore the more remote parts, allowing time for ferry crossings and delays; time to follow up the brown and white daisy-route signs that will lead to the most scenic areas; time to be amazed that no one has yet done a proper PR job on this surprising little country.

Wandering aimlessly into the gentle countryside in a rental vehicle, we found ourselves blinking against the midsummer glare of fields of red poppies spilling across the low hillsides and into small valleys. Our cameras did overtime as we snapped poppies and windmills, thatched houses, and more thatched houses. We hopped on a ferry to the neighbouring island of Fyn and wondered why hadn't we been told how truly lovely this place was?

It rained too, as it does there. Danes joke about their weather as much as the Brits, it seems. Danish humour is uncomplicated and self-depreciating and we found their optimism catching. And if the rain really is a problem, you just light some candles and enjoy some hygge. Two things are central in Denmark. Design, an individual style typified by exquisitely crafted glass, silver, pottery and amber with a clean, fluid Scandinavian economy of line that makes you gasp; and hygge – of course.

Denmark is a bright shiny little clockwork country. It works as perfectly as if someone winds it up tight each night so it can just run itself, with no fuss or bother, all day. Trains arrive on time, and they are clean, officials are polite, factories pump out their expected quota, and everything just seems to work. And the people, at least on first acquaintance, seem to have combined some of the more positive attributes of their neighbours while dropping the negatives: so you see German efficiency, the spick-and-span orderliness of the Dutch, and the sexiness of the French. If you doubt the latter, remember Denmark was the country that legalised pornography. 

But that was over 25 years ago. A couple of years ago Copenhagen was selected as the cultural capital of Europe. The Danes accepted the honour and a responsibility with pride, and scheduled dozens of artistic, musical and historical events throughout the year. But culture is no newcomer here. Since 1843, the Tivoli Gardens have been the musical centre of Copenhagen, and each summer the Concert Hall, which now seats 2000, welcomes soloists, conductors, orchestras, ballet and opera companies, and choirs from all over the world.

When you think about it, the Danes have already contributed much in many areas – Hans Christian Andersen, Hamlet, Karen Blixen (the author of 'Out of Africa') philosopher Kierkegaard, Bohr the developer of the quantum theory, and not least Danish cheese and bacon and Lurpak butter that turns up on tables throughout the world. Others would cite Georg Jensen for his silver work and Royal Copenhagen porcelain. Many would simply opt for Carslberg beer as Denmark's greatest contribution to society.

But beer is not the only amber claim to fame here. The hard stuff, real amber, is washed up on beaches throughout Scandinavia and the Baltics, churned up further north. Some believe icebergs release the petrified resin from its millenniums-old hiding places deep on the seabed. This ancient substance is set by skilled craftsmen in gold and silver, or strung in wanton excess and festooned in shop windows throughout the city. The biggest surprise is that amber is not always amber. It glows gold and tawny of course, yet can just as easily be opaquely lemon or brown, almost black sometimes. 

Scratch a Dane and you find a performer. Their relaxed good nature makes them natural extroverts and you find them everywhere. Stroll down Strøget, the 1.5 kilometre cobbled pedestrian-way threading through Copenhagen's main shopping area, and you will be entertained by mime artists, painters and musicians. Drop into Tivoli, a playground for everybody and a must-see for all ages, and they are there at the fun-booths, manning the gates for the rides or up on centre stage. We found one huge blonde fellow curled up in cowboy gear on a ferry seat, catching a nap on his way to a gig on Fyn. Victor Borge was not alone. Sometimes, it seems there's a country full of them.

Denmark is basically a safe country too, although the locals will wag their heads deploring the latest crime wave. Bike stealing. Despite this, there are certainly still plenty around. Most major roads have bike lanes painted onto the footpaths, and cyclists jealously defend their rights.

My first day in Copenhagen I was yelled at in Danish for presuming to walk in a bike lane. That same day  I located a bedding shop in an arcade off Strøget. I wanted to buy a doona and pillows filled with the softest down, my special Scandinavian souvenir. My hygge.

But not only that. It was so that, when I sleep, I can dream of Denmark. Of course!