That is the eye-catching accusation in the Guardian, following a report in a trade publication, the Bookseller.
Amazon will not confirm that it has managed to do this.
The accusation hinges on the fact that since 2006, its UK business has been a subsidiary of its European headquarters in Luxembourg.
As a result, anyone buying anything from Amazon in the UK makes a payment to the retailer in Luxembourg, with the profits taxed there rather than here.
That is despite the fact that Amazon employs hundreds of staff in the UK, at several large depots, selling tens of millions of items each year to millions of UK customers.
"Amazon EU serves tens of millions of customers and sellers throughout Europe from multiple consumer websites in a number of languages, dispatching products to all 27 countries in the EU," Amazon said.
"We have a single European headquarters in Luxembourg with hundreds of employees to manage this complex operation."
Campaigners against tax avoidance arrangements - which are in fact quite legal - have taken a very dim view of all this.
Speaking on BBC Radio 4, Richard Murphy of the Tax Justice Network said the government had turned a blind eye to this sort of thing and was even encouraging it.
"I severely criticise our tax authorities for putting up with this sort of arrangement," he said.
"It is part of our "open for business" agenda - we will let a multinational company do what it likes, so long as they put some jobs in the UK, but we won't ask for tax."
In fact, HMRC has long had a specialist unit of 1,200 tax inspectors dealing just with the affairs of the 770 biggest companies.
It is called the Large Business Service for firms with a turnover of Â£600mn or more, or assets of Â£2bn or more.
"We can't discuss Amazon for legal reasons, but HMRC applies the tax laws as they apply to multinationals so the UK receives the tax revenues to which it is legally entitled," HM Revenue & Customs (HMRC) said.
"Where there is a high risk of the UK losing out, we move our resources to challenge that risk," it added.
When it comes to multinationals and tax authorities arguing about how much tax should be paid, and to whom, the arguments often last for years, frequently hinging on a concept known as transfer pricing.
This occurs when a division of a multinational in one country charges a division of the same firm in another country for the supply of a product or a service.
This is sometimes criticised as a technique in which artificially high charges are levied internally, with the aim of siphoning money from a firm's business in a high-tax country to a low-tax one.
There is nothing new in this problem and the issue hit the headlines in the UK as far back as the 1970s.
There is now a lot of legislation to stop transfer pricing being abused, but in the end, there may be no right answer to how much tax is owed by a firm, and a settlement can all come down to haggling.
One tax adviser at a leading firm of accountants - who wished to remain anonymous - said it was wrong to suggest the UK tax authorities were just sitting on their hands, watching taxable income move abroad.
"There are some very bright people at HMRC scrutinising these sorts of things, it is wrong to assume we are lax at policing this."
Another commonplace technique for multinationals to lower their tax bills - a variation on the transfer pricing theme - is for the head office in one country to charge all the national subsidiaries a large fee for "management services", such as accounting.
If the fee is legitimate, then it is an allowable expense and can be set against a national division's profits to reduce its tax bill, while cash is transferred from that outpost to the head office.
Ronnie Ludwig, a tax adviser at Edinburgh accountants Saffery Champness, says the arrangement is commonplace.
"It is perfectly legal for a company to levy a management fee on a subsidiary," he says.
"The question is whether it is proportionate and reasonable in relation to the actual services provided - the companies will be asked by the HMRC exactly what they are doing to justify the fees," he added.
For its part, Amazon says in its accounts that it may have to pay an extra $1.5bn in back taxes in the US if it loses various transfer pricing disputes with the tax authorities there, going back to 2005.
Amazon's accounts, filed at the United States chief financial regulator, theSecurities and Exchange Commission (SEC), also make it clear that is facing investigations of some sort from several other national tax authorities.
"We are also subject to taxation in various states and other foreign jurisdictions including China, Germany, Japan, Luxembourg, and the United Kingdom [and France]," the accounts say.
As a result, the company has set aside $229m to pay any extra tax bills that may now arise from these.
"Everyone of these jurisdictions is going to be very jealous of its entitlements to get tax," says Philip Spencer, a tax partner at accountants BDO.
"It is commonplace to have lots of investigations on the go at any one time."
Multinational firms will inevitably look for a good central site to administer their businesses in a region, not just for a low-tax regime, but to get good staff and enjoy good communications.
It all makes life easier.
Philip Spencer at BDO points out that a key advantage of a country like Luxembourg is that it also has a good network of double-taxation treaties with other countries.
These regulate the taxation of cash flowing from business activity in one country to another.
"Luxembourg is very favourable, it has lots of these treaties, which help avoid having to pay tax in one country and then reclaim it if tax is also levied in a second country."
A key feature in all this is that the internationalisation of business has been give a huge boost by the advent of the internet and online trading.
And this has made life increasingly hard for national tax authorities to deal with.
"What everyone is grappling with is e-commerce," says John Whiting, tax policy director at the Chartered Institute of Taxation (CIOT).
"Everyone can see that firms like Amazon are making a shedload of profits - the question is where the profits were made."
Has the giant online retailer Amazon managed, quite legally, to avoid paying any corporation tax at all to the UK in the past year?