Forget the Tate Modern or White Cube. To get a real taste of the bleeding edge in British art, you need to head south of the river, to the backroom of a pub, or the roof of a multi-storey carpark.

For years, when the name of Peckham, a district of southeast London, was mentioned, people thought of two things. First, Del Boy Trotter, the fictional dodgy dealer who was the area's most famous resident thanks to the hugely successful 1980s BBC sitcom Only Fools and Horses. Second, gang culture and teenage knife crime.

Foreboding council estates and concrete tower blocks overlook rundown high streets full of fried chicken shops and stalls offering knock-off mobile phones. It is  a ghettoised place, ridden with poverty and violence. This was the London that tourists never saw, with good reason.

But while Peckham had – and still has – its problems, the stereotypes never quite rang true. Nearby Camberwell College of Arts and Goldsmiths University have long brought a steady stream of art students, lending a bohemian edge to the area. And in just the past three years, the artistic revival has really stepped up the pace of change . Increasing rents in Hackney, the east London borough that has been home to the capital's creative community for the past 15 years, have begun pushing artists south of the river, and the epicentre of London's art scene has started to shift with them.

“Peckham's definitely become the name to drop,” said Jo Dennis, who runs the local Asylum Arts gallery. “A lot of my artist friends used to pretend they didn't even know where southeast London was – now they're all planning to move here.” To celebrate the burgeoning scene, Art Licks, an independent website and magazine, has set up a Peckham art tour that introduces the area's teeming creative riches to a wider audience.

The tour starts at Peckham Space, a community-run gallery that aims to engage local young people with artists. The most recent exhibition was a film project by David Cotterrell, titled Slipstream. He attached a camera to a remote control helicopter and flew across the new build apartment blocks of North Peckham estate, filming the journeys once taken by residents along the now-demolished elevated walkways that linked tower block to tower block.

Across the street from Peckham Space is the Bun House pub. Its main room is full of grizzled men supping pints of bitter, playing pool and watching a TV blaring out horse racing. It is the kind of place where you would suspect a dismissive reaction to Modern art. But step through to the back room, and an exhibition by Austrian artist Ulli Knall appears – a sculpture made of napkins and bottle tops, shards of broken tiles on the walls. Outside, a quick clamber up a wall ladder to the roof reveals a sculpture made of duvet covers and pillow cases, twisted on a stool. On a recent visit two men were having a pint next to it. “No, we're not the artists,” one laughed. “We're just having a drink.”

It is this juxtaposition of the quotidian with the bleeding edge that makes the Peckham scene so refreshing. This is an art scene actively engaging with its surroundings. At the Son Gallery, a minimalistic white room in an industrial warehouse, the evangelical exertions of a preacher at a nearby Pentecostal church might be heard as artist Joschi Herczeg talks about his work.  Panels of black glass hang from the ceiling and blowing hot breath on them, he explained, reveals engraved hidden messages. Around the corner, the Methodist church agreed to allow artists to use its aisles for a new exhibition.

The final stop on the tour is Bold Tendencies, a literal totemic symbol of Peckham's art-driven resurgence. The top two floors of a miserable grey carbuncle of a multi-storey car park have been transformed into a sculpture gallery. The space is made cooler with the addition of Frank's, a cafebar that is fast becoming the one of the most popular new hangouts in the capital. The views across the city are worth the visit alone. Works from 14 international artists are scattered across the concrete. Huge metallic claws resting on uplit pedestals compete for attention against giant inflatable rats singing love songs to each other and a boardwalk twisted into rollercoaster-like hoops by a pallet truck. 

The last exhibition on display, a battered, custard-yellow Robin Reliant van, with the legend “Trotter's Independent Traders” emblazoned on the side, confirms why Peckham needs to be added to any tourist's London itinerary. The recognisable three-wheel vehicle belongs to Del Boy Trotter and artist Jess Flood-Paddock added the words “London-New York-Peckham”. It is a humorous, poignant bringing-together of Peckham old and new, a hitherto unloved working class urban district on the verge, perhaps, of achieving international prominence.