A sleazy shop assistant seduces a vulnerable colleague for a money-spinning sex tape; two hopelessly-in-love students are brutally murdered by the girl's family; an intrepid TV reporter embarks on an expose of the notorious casting couch. This triptych of stories set in 21st-century metropolitan India unfolds over 98 minutes of blurry, trembling CCTV, mobile phone, camcorder and hidden-camera footage in the film LSD: Love, Sex Aur Dhokha (Love, Sex and Betrayal).

Surely the only Indian film to reference sex and drugs in both its title and abbreviation, LSD: Love, Sex Aur Dhokha is one of the new wave of Indian indies – edgy, off-beat films challenging the stereotype of Indian cinema as tear-jerking, all-singing, all-dancing Bollywood. It fared more than respectably when it was released in India last year, making £1.25m from its paltry £200,000 budget, and was selected to open the inaugural London Indian film festival (LIFF) in 2010, and thereby act as the flagship for this fledgling cinematic phenomenon.

In fact, 2010 proved decisive in the breakthrough of Indian indies (or "Hindies" as they have been dubbed in India) into mainstream cinema: LSD and Peepli Live, a deliciously dark satire on media, politics and farmer suicide, made India's top 10 most profitable films of 2010 in percentage profit, while Dhobi Ghat, an elegant paean to old Bombay, and the slapstick of Tere Bin Laden were critically lauded and box-office successes in the key "metro cities" (Delhi, Mumbai, Chennai, Kolkata and Bangalore).

Considering the eye-watering losses incurred by big-budget Bollywood flops such as Kites, Raavan and Veer, it's no wonder the Indian film industry has woken up to the possibilities of low-cost independent films starring virtual unknowns and directed by emerging talent. Indian indies have been given a helping hand thanks to the patronage of Bollywood superstar Aamir Khan, whose production company Aamir Khan Productions (AKP) is responsible for Peepli Live, Dhobi Ghat, 2007's sleeper hit Taare Zameen Par and the forthcoming caper comedy Delhi Belly, which premieres at this year's LIFF before getting a general release.

Khan has become the figurehead of Hindie cinema more by luck than design. "AKP began by accident. I didn't intend to produce films until I came across the script for Lagaan – which I loved, and nobody was prepared to produce. The industry thought a film about villagers rising up and playing cricket against the Raj was too unusual and very risky. Since Lagaan it's been 10 years and we've produced six films, and they all have been films nobody else would touch," he says. "Of these five have been first-time directors and two have been women directors, which is unusual in India. So we're a production house for young talent and film-makers who want to do different films. Each of the films is off beat and alternative, so unintentionally we have ended up supporting independent cinema."

The fact that 46-year-old Khan is one of Bollywood's top three actors (along with two other Khans, Shah Rukh and Salman) and star of the two highest-grossing films in Indian cinema, 2009's 3 Idiots (£47m), and Memento-inspired Ghajini (£26m), and 2001's Oscar-nominated Lagaan – the third Indian film to be shortlisted for an Academy award – has made the public and industry sit up and take notice of Indian indies.

Cary Rajinder Sawhney, director of LIFF, as well as curator of South Asian content at the London film festival, has high hopes for Delhi Belly. "We moved the festival to tie in with Delhi Belly's release, as we knew it was right for our audience. Rather than the standard Bollywood audience across four generations, we're aiming for the younger generation who are disenfranchised by Bollywood of their parents' era, and want something more cutting-edge," he says.

Delhi Belly certainly fits the cutting-edge bill – it's in English, and has an Adults Only rating in India for swearing and depicting sex. Despite being a household name with a family-friendly image, Khan makes no apologies for backing it. "In genre terms, it's like Lock, Stock and Two Smoking Barrels, and reflects audiences are changing, and so are film-makers. The writer studied film-making at UCLA and the style of the script is western. Indian cinema is evolving."

Sawhney began LIFF to showcase the fact that Indian cinema has more to offer than Bollywood. "As programmer for the London film festival for 15 years, what struck me is how few of the Indian films were picked up for distribution in the UK, or were critically acclaimed."

The two-week event aims to broaden the UK's narrow view of Indian cinema not only through smart programming but also through organising industry workshops between British and Indian film-makers. "We see Iranian or Latin American film lauded at film festivals, yet good Indian cinema is going under the radar," Sawhney says. These films should be taken as seriously as other world cinema. In the UK it seems the only conception of Indian cinema is Bollywood or Satyajit Ray. There's been a real surge in new-wave independent cinema, and it's successful in the box office."

Indian independent cinema is a different beast to Hollywood. In India all producers were independent, big or little, until the government granted Indian cinema "industry" status in 2001. This ushered in the era of corporate studios such as Reliance, Eros and UTV, which finance, produce, distribute and market films. (One result of the change was that film-makers no longer depended on the underworld for finance.)

Film critic Anupama Chopra says the term independent cinema applies, in India, to a film's creative sensibility. "We're not talking about finance or distribution, but content and storytelling. These films don't adhere to the song-and-dance formula we've had for many years," she says.

India does have a history of arthouse cinema, even if Bengali director Satyajit Ray is the only film-maker most have heard of. "There was a vibrant art house or parallel cinema movement in the 1970s and 1980s," Chopra, says "with directors like Shyam Benegal and Govind Nihalani, and brilliant actors Naseeruddin Shah, Shabana Azmi and Smita Patil. The cinema was challenging, but only occasionally did well commercially.

"It petered out in the 1980s because audiences stopped going to the cinema because of video. The resurgence in independent cinema is not arthouse in the way we knew it. Now they're not stories of rural India or exploitation; instead we have a whole generation of directors raised on Bollywood and Hollywood, telling modern urban tales."

As with any story on contemporary India, globalisation and the opening up of the economy have been pivotal: "Modern film makers have grown up with satellite TV. It arrived in 1991; before that there was one state-run channel. People who are 20 to 25 have grown watching The Bold and the Beautiful and The Sopranos."

In 1997 the first multiplexes arrived (housed in air-conditioned shopping malls) and their rapid proliferation has contributed to the development of more sophisticated, broader tastes. "Before multiplexes," says Chopra, "you only had single-screen cinemas seating 1,000; to fill that you needed a big movie. Now you can put the big movie in a screen with 500 people and something like LSD, Peepli Live or Delhi Belly in a screen for 200 or even 90 people. Both will sell out."

The corporate entities, such as Reliance BIG Entertainment, haven't hesitated to move with the changing times, and are increasingly prepared to enter into co-productions with independent operators. "One third of the population is under 25," Mahesh Ramanathan of Reliance says. "Changing societal patterns are influencing cinema, and films made on small budgets that mirror today's youth and lifestyle can also turn in big box-office numbers."

That's not to say the age of big-canvas, megastar-led, pan-India blockbusters – the four-quadrant film appealing to young and old, male and female – is over. But the financial risk means they will be few and far between, part of a film industry that's more agile, varied and innovative in its storytelling."What's been good to see in the last few years is there have been different kinds of films being made," Khan says. "Rather than one kind of film, there's a variety that speaks for the health of the industry going forward."

• Delhi Belly screens on 30 June as part of the London Indian film festival (londonindianfilmfestival.co.uk), which runs until 12 July. Delhi Belly goes on general release on 1 July.