Half a dozen young ladies, not naturally blonde, wearing knee-high boots, are chain-smoking round a lamppost. "They used to stand right outside," says Peter, manager at new organic diner Bio Mio, where we sit straining, rather shamefully, for a better view. "But their clients didn't like being seen, so now they have moved further down the street."

Of course, Copenhagen is famed for its liberality (current slogan: C[Open] Hagen), and we are in Vesterbro, the red-light-cum-hipster district, but such blatant solicitation is still a little eyebrow-raising. And, as we soon discover, it's a subject the locals can't seem to stop talking about either: checking into the Bertrams Hotel, I point to the area's best-known street, trendy Istedgade, on the map, asking if we should head there first. "It's full of hookers at that end," says the man, covering half the street with a sausagey finger. "And there are quite a few down there, too."

The more people we meet, the more I realise how proud the locals are of the area's ruggedness, its diversity. "Rich people don't come here, and that's fine by us," says student Heidi, at style bar Bang & Jensen, before dragging us over, shell-shocked at paying £6 for a pint, to hear unrepeatable stories about its roughest corners: "If you're wearing flip-flops," she says, with a laugh, "you might be lucky and step on a needle."

Even the audio walking guide from the City Museum on Vesterbrogade features X-rated tales, narrated by poet Claus Handberg Christensen, of prostitutes, junkies and drunks (unimaginable, surely, in an official guide to London).

So the undercurrent is still there, pulling at Vesterbro's gathering gentrification. Although traceable back to Copenhagen's year as European City Of Culture in 1996, when the cattle market, Oksnehallen, was converted into an exhibition hall, the real catalyst for the revival of the fortunes of this working class area came a year later, when the scruffy-chic Bang & Jensen bar opened on former "meat street" Istedgade.

"It was bad in Vesterbro back then," says bespectacled owner Morten Bang, who grew up here. "We had to do something, and when an old pharmacy went bankrupt we knew we could make it an instant success." More surprising was that owners of neighbouring sex bars offered support: "A big tattooed man came in just after we opened with a bunch of roses and said, 'I am from Spunk Bar. I hope you survive'."

The sleazier side to Vesterbro stops abruptly at the junction between Istedgade and Gasvaerksvej: thereafter, the streets (particularly the funky Oehlenschlagersgade) bustle with boutiques, homeware stores, galleries, bars and cafes. The dining scene has been evolving too, spearheaded by the Cofoco (Copenhagen Food Consulting) team, which owns five restaurants (cofoco.dk), including one, Les Trois Cochons, on top foodie street Vaernedamsvej. The street is also home to the atmospheric Falernum, which matches wine to Danish "tapas" such as black risotto with tiger prawns, and herring in breadcrumbs).

The newest places in Vesterbro play to the citywide obsession with all things organic: at the 200-seat Bio Mio, converted from a 1920s Bosch warehouse, you sit at a shared table, order at the counter (we enjoy tenderloin pork with red cabbage and butternut squash) and watch a chef cook it in five minutes. Not that relaxing, perhaps, but you are immersed in the neighbourhood buzz. A word of warning: eating out costs dearly, with main courses often around £20.

The most significant developments are in the "White Meat City" section of Kodbyen, the hard-to-find meat-packing district. We walk past Bio Mio (recognisable only by its illuminated Bosch sign) and turn left by the faded Chicky Grill, past piles of crates and wooden boxes, into a huge car park surrounded by white-and-blue buildings suggestive of classic ocean liners. We visit two new galleries, Hans Alf and DASK, both created from former refrigeration units, but the regeneration's heart is Bo Bjerggaard, the first gallery to move here from central Copenhagen, 18 months ago. Its spacious white rooms now host 10 international exhibitions a year.

Next to dive bar Jolene on Flæsketorvet, is the jewel in the "Flesh City" crown: gallery/restaurant/bar Karriere, owned by siblings Jeppe and Laerke Hein. Customers lounge outside in the spring sunshine. Inside, over cocktails with Nordic herbs and flavours - verbena, liquorice, aquavit - Laerke explains that the whole venue is an artwork.

The bar moves slowly from side to side, the lights are by Olafur Eliasson (famous for his Weather Project at Tate Modern) and if nature calls, don't expect an easy ride: "There are 25 doors but only five toilets," Laerke says. "Some people wait patiently outside one that will never open. It's about losing a bit of control."

• SAS (flysas.com) flies to Copenhagen from London, Aberdeen, Manchester and Birmingham.

Vesterbro address book

Axel (7-11 Helgolandsgade; 00 45 33 313266; hotelguldsmeden.dk; doubles from £165) This is an elegant palace of Danish chic, with blond parquet floors, wicker chairs, friendly staff, a loungey garden, and labyrinthine spa. Stylish Bertrams Hotel on Vesterbrogade is in the same chain (hotelguldsmeden.com).

Bang & Jensen (130 Istedgade; 00 45 33 255318; bangogjensen.dk) Fun kitschy cafe with old pinball machines and football tables, serving its young clientele with coffees and a special all-day breakfast by day, and cocktails at night.

Designer Zoo (137 Vesterbrogade; 00 45 33 249493; dzoo.dk) A collective of eight designers with studios in a former sausage factory sell enviable furniture, jewellery, glass, ceramics and knitwear.

Sorte Hest (135 Vesterbrogade; 00 45 33 252008) The simple spaces of the "Black Horse" play host to new Vesterbro cooking at its best: try the scallops and cauliflower and cod with mushrooms.

Art Rebels (17-19 Flaesketorvet; 00 45 26 223373; artrebels.com) Blink and you might miss this tiny outlet for young designers' clothing, art and music.

Dyrehaven (72 Sonder Boulevard; 00 45 33 216024) Formerly an infamous bodega (pub) nicknamed "Acid Haven", this is the district's latest hang-out and has been christened by scene godfather Morten Bang as the new Bang & Jensen.

Bio Mio (19 Halmtorvet; 00 45 33 312000; biomio.dk) Friendly and noisy organic restaurant. The menu indicates good sources of vitamins and minerals.

Karriere (57-67 Flaesketorvet; 00 45 33 215509; karrierebar.com) Quirky bar that says it will "put a smile on your face" with drinks and cocktails created from local and seasonal ingredients.

Bo Bjerggaard (85A Flaesketorvet; 00 45 33 934221; bjerggaard.com) International modern art gallery, specialising in European art, photography and video installations.