On the face of it, it was a week in which the great rock'n'roll swindle was in full swing. On Tuesday night – representing the popular end – Take That were crowned best British group after a performance that left them in little more than their underwear. On Friday, serious musos got their chance to indulge when they were able to download The King of Limbs, the latest Radiohead album direct from the band's website from £6.

Yet, underneath the glamour, and despite all the hype about the digital revolution, the music business – as represented by the major record labels – is in serious financial trouble. Sales were down 7% last year in the UK and by nearly 10% in the United States, the world's largest music market. Two of the four music majors, Sony – home to Simon Cowell – and Warner Music, behind Cee Lo Green and Plan B, admitted their pre-Christmas sales were down 10% and 14% respectively.

It has been a decade since piracy and the arrival of iTunes – which destroyed the notion of an album in favour of single, downloadable tracks – but the music business has found nothing to repair lost CD sales. Arcade Fire's The Suburbs may have been album of the year at the US Grammy Awards last weekend, and winner of the international album prize at the Brits on Tuesday, but it has sold only 1.4m copies worldwide. "Wind the clock back a few years and that would have been 4m to 5m," says the Canadian indie rock band's manager, Scott Rodger.

What has emerged is, on the face of it, a nightmare scenario. The music industry has roughly halved in size since the last days of the CD-fuelled peak, when boyband *NSync's No Strings Attached album could sell more than 10m copies in 2000 – but the hope was that one day, digital sales would pick up the growth as CD sales – or "physical" sales, as the industry likes to call them – levelled off. However, in the US, from where all music business trends start, download sales growth has all but stalled, posting just 1% growth throughout all of 2010.

"The record industry is now in a very serious situation," says veteran protest singer Billy Bragg, who lobbies for the rights of performers through a body called the Featured Artists Coalition. "Partly these are problems of the industry's own making, but the result is there is no longer, for example, the record-shop culture that has proved so important at the start for so many musicians." Nor is it just small record shops that are in trouble – the fall of Woolworths and Zavvi has been followed by problems for HMV – which last month said it would be forced to close 60 stores in the wake of a profit warning following poor pre-Christmas sales.

Yet, for all the downwards sales figures, there are plenty in the music industry who remain, if not optimistic, then at least hopeful.

While Take That, with Robbie Williams, may be one of the very few bands that can still sell large quantities of CDs – not least because as their record company, Universal Music, found, their mainly lower-income, older female fan base prefers not to download songs online – it is Radiohead that point the way to the all-digital future.

Radiohead released The King of Limbs as a download on Friday – their second album since the band walked out of EMI in 2007, following a row in which they had tried and failed to persuade EMI to hand them control of the copyrights to their first six albums, including the landmark OK Computer. Their first album as an independent band, In Rainbows, was sold via an "honesty box" approach in which people could donate whatever they thought the album was worth – but was priced at £6 for an open format MP3 download or £9 for a higher "CD-quality" WAV format file.

Last week, manager Chris Hufford described the new pricing strategy as a "logical progression" from the honesty box approach, but the band's decision shows they believe theirs is an ideal minimum price point for their work. Plus, in a clear sign of the impending demise of the CD, a physical release of the album won't appear until next month – with a special edition, comprising a CD, two 10-inch vinyl discs and a host of artwork going on sale for the healthy price of £33.

The Radiohead approach can't work for every artist – an X Factor winner is unlikely to be able sell a £33 album – but to succeed in the new arena, artists have to embrace any form of internet marketing they think is appropriate, and record companies know they have to adapt. Last year Ellie Goulding, who likes to run almost as much as she likes to sing, hooked up with Nike, and through her Facebook pages invited a small number of selected fans to run with her in seven different cities on her UK tour.

Her record label, a Universal subsidiary, Polydor, then released a remixed version of Lights, aimed at providing a running soundtrack, in an effort get Goulding's music taken up by the national running subculture. "It took us out of the traditional record promotional cycle, based on peaks of activity around a record release and meant that she was being marketed over the whole of last year," said Paul Smernicki, the director of digital for Universal Music.

In the new era, the digital relationship has become critical as the retailers crumble. Tony Wadsworth, the chairman of the BPI, the trade body for the record labels, said: "Ten years ago all we did was make plastic and sell them to record stores. Now, in a business where over a quarter of sales are digital, we need a much broader combination of ways to make money."

Many hope that music subscription services, such as Spotify in Europe and Pandora in the United States, can generate new, meaningful forms of revenue. Spotify has more than 500,000 paying customers to its £9.99 a month all-you-can-listen-to service – but that £60m-a-year business is still modest when set against a business that still generated $17bn for record companies worldwide in 2009, the last year for which statistics are available. Meanwhile, other streaming services, such as Sky's Songs service and Nokia's Comes With Music, aimed at its mobile phone customers, have flopped – so the creation of a mass music subscription market is not yet assured.

What is also clear is that in the new environment, the music business is becoming increasingly polarised between pop acts pushed by the likes of Simon Cowell through the medium of television, and the acts that have taken considerable risks to hang on to what they believe is their artistic credibility. But while the best pop can still sell, as Take That showed with Progress, their last album, which was the bestselling British album since Oasis's Be Here Now in 1997 – it is the more indie acts that have to be particularly astute to navigate the faltering commercial system.

Arcade Fire, for example, invested their own money into their early records and videos – with the result that the band was in a stronger bargaining position when major labels became interested in them. Their manager, Scott Rodger, says: "When we sell 1m units we get the income equivalent to 5m units for a band in a traditional record company deal," but he acknowledges that it is an approach that is difficult to pull off.

Even established names wonder at the values of the new musical economy. Billy Bragg said: "I've recently recorded half a dozen new songs – and I gave them away on my website. Meanwhile, I've got six different types of T-shirt that I sell for about £20 a time when you add in postage. I have to say I sometimes wonder what business I'm in."