The deal that the iPad maker struck with publishers could be threatened by an inquiry into the prices people in the EU pay for their digital reading

For book publishers, Christmas will come twice this year. After the festive trade in hardback tomes, the celebrations will begin again on Boxing Day, as the millions who got Kindles from Santa go online to stock them with reading material.

Amazon already sells more ebooks than paperbacks. It claims sales of Kindle devices have reached 1m a week, while 13m iPads will find a home this quarter. Juniper Research forecasts 25m e-readers sales globally this year, and 55.2m tablet sales.

The British bought 12.7m ebooks in the first half of 2011, double the amount for the same period last year, according to the Publishers Association. By common consent, January will be a record month for digital books.

But regulators, both in Europe and the United States, are worried that shoppers may be overpaying. This month, both the European commission and the US department of justice have announced investigations into ebook sales. They are to lift the lid on a power struggle between the publishing industry and Amazon that could determine the shape of the book trade for years to come.

The European commission will probe the "agency" deals signed between Apple and five of the biggest publishers: Hachette Livre, Harper Collins, Simon & Schuster, Penguin and Macmillan.

The trouble began in early 2010. Worried about declining physical book sales, publishers feared Amazon's eye-catching discounts would devalue their electronic product. So they agreed to a business model proposed by Apple just before the release of the first iPad. It was a move intended to force the world's largest bookseller to relinquish control over pricing.

The agency deals apply only to digital books. Publishers set the retail prices and bookshops take a 30% cut on each copy sold. The model was designed by Apple, but subsequently forced on Amazon, and has been adopted mainly in the UK and US, by Waterstones, Canadian group Kobo and Barnes & Noble.

"The whole point of the agency model is to prevent the emergence of monopolists like Amazon," says Benedict Evans, a digital media expert at Enders Analysis. "What the publishers have done is stopped Amazon from crushing the independent ebook retail sector."

Amazon has lobbied furiously against the agency model. European regulators fear consumers may be paying too high a price to keep the American retail superpower at bay. "The commission has concerns the publishers may have colluded to raise the price of ebooks and that Apple may have facilitated this," says the commission's competition spokeswoman, Amelia Torres.

Agency deals will also come under scrutiny in US courts. Law firm Hagens Berman is bringing a class action suit in California against Apple and the big five publishers on behalf of book buyers. Founding partner Steve Berman says: "In the US, we believe that the publishers and Apple got together and agreed to fix the prices, and you are not allowed to do that. As a result, prices of e-books have exploded, jumping as much as 50%."

Publishers are reluctant to speak publicly but deny any collusion, saying they met Apple individually, rather than as a group. The agency model, often used for reselling insurance or software, is a well-established system enshrined in European law. But prices have risen since it was applied to ebooks.

Amazon no longer charges its old flat rate of $9.99 for new titles in the US; bestsellers now average $15. Berman says shoppers are paying between 30% and 50% more. Some ebooks now cost more than the hardback. Walter Isaacson's biography of Steve Jobs is a contender for the bestseller of the year. It retails on Amazon for £10.77 as a hardback and £12.99 in digital format. At waterstones.com, Ken Follett's Fall of Giants, another top title and a very thick book, is marked at £5.38 as a paperback and £8.63 for download.

Digital books cost less to produce, transport and store, and these savings may not have been passed on to readers. Mass-market paperbacks are usually sold at the same price in paper or e-ink. And yet a $7.99 ebook will generate a profit of around $3.80 for a publisher, under the agency model. The margin shrinks to $2.25 for the physical version.

With ebooks available a year ahead of paperbacks, readers are often prepared to pay for instant gratification. In the UK, publishers say any saving is taken by HM Revenue & Customs. While paper books are untaxed, ebooks attract 20% VAT.

"The whole industry was worried about what Amazon would do once it got into a dominant position," says Philip Jones, deputy editor of the Bookseller. "Publishers used the agency model to deflect its progress and it has worked."

There are no official figures but industry sources say that in the past year, Amazon's share of the North American ebook market has fallen from around 80% to 60%. Barnes & Noble, which has its own Nook e-reader, said in June that it had taken 27% of the US market. Apple's iTunes is in third place, and in fourth position, with perhaps 5%, is Canadian retailer Kobo, whose e-readers are now on sale here at WH Smith and Asda. Amazon's UK share is at around 70%. Waterstones, which won't have an e-reader until next year, has slipped from 20% to 10% in the past year, while iTunes has bagged 15% to 20% of sales.

Publishers believe Amazon is no longer dependent enough on their industry to care about its wellbeing. Founded by Jeff Bezos in 1995 as an online bookstore, it now earns more money from shifting a panoply of nappies, TVs and golf clubs than it does from books, video and music. Last year, general merchandise accounted for $18.4bn of sales, compared to $14.9bn for media.

Books are Amazon's shop window rather than its cash cow, say publishers. When Amazon discounts paper books to below the wholesale price, it takes the hit. Should the retailer become too dominant, it could start forcing publishers to lower their margins.

Bezos has already flexed his muscles. In January 2010, Macmillan chief executive John Sargent went to see Amazon in Seattle to present agency terms, then flew home to New York. By the time his aircraft landed, every last Macmillan title Amazon stocked had been withdrawn from sale. The stalemate lasted a week.

Regulators must now decide whether agency agreements are a legitimate way to fight back. "It would be good for the industry to have clear guidance on what the legality is of these arrangements," says competition lawyer Alexandra Kamerling at DLA Piper.

Without competition between retailers, downward pressure on prices could still come from competition between publishers. But the UK banned the Net Book Agreement in 1997 after judges decided letting publishers set fixed prices was against the public interest. Large retailers like Dillons and Waterstones had in any case found loopholes. Damaged books could be discounted, so they deliberately defaced stock.

Most online bookshops are classic retailers, independent businesses used to setting their own prices. Sanctioning a model which sees them indefinitely handcuffed seems untenable. But a decision against the publishers could take the cheer from Christmas future for an already fragile book industry.