On 27 April 2000, after seven tense weeks, the British government's largest ever auction of a national asset came to a spectacular end.

In the dizzy days of the dotcom boom, five mobile phone networks had offered to pay a total of £22.5bn for the right to operate the 3G licences that would bring the internet to mobile phones.

"Ministers feared they had bankrupted the mobile industry," says an official who worked for the Treasury at the time. However, while the ability of networks to invest in the masts needed to broadcast 3G around the country was undoubtedly hampered, 13 years later it is the British taxpayer rather than the industry that is counting the cost.

A Guardian investigation has found that the generous tax breaks afforded to companies under British law means that while the UK's mobile networks are already handing out fortunes to their shareholders in dividends, three of them are still paying little or no tax.

Everything Everywhere (EE), Britain's largest network with 26 million customers, has in effect never paid corporation tax, despite generating £19bn in revenues since it was created through the merger of T-Mobile and Orange three years ago. Its corporation tax bill was £1m in 2012, but that was offset against £90m in tax credits from HMRC for the previous two years.

The company has been able to claim money back from the taxman despite passing £3.25bn in dividends and fees to its parents, Deutsche Telekom and Orange (previously France Télécom), during its lifetime. This is more than the annual NHS spend on maternity wards, or on accident and emergency services, in England.

This is because British law allows relief on a quarter of the money spent on items including debt interest payment, spectrum purchases and installing equipment such as masts and radios. The relief is equal to the tax rate – an average of 25% in recent years.

Meanwhile EE remains committed to generating a substantial annual dividend. Under the joint venture agreement between Deutsche Telekom and France Télécom, the new company intends to pay 90% of its annual free cash flow by way of dividends.

EE explains that it is not funnelling profits to low tax jurisdictions, and that its parent companies pay the tax due in their home countries of France and Germany. The firm says it is considered low risk by the UK tax authorities, indicating that it follows both the letter and spirit of the law.

But critics say that its ability to send large sums abroad while making no corporation tax contribution to the Exchequer highlights the unfairness of British laws.

"The case of the telecoms industry shows the folly of the current corporate tax regime, which allows companies to structure their affairs in ways that add no economic value but reduce their tax bills," said Prem Sikka, a tax expert and professor of accounting at the University of Essex.

Vodafone makes full use of relief on loan payments to minimise its tax. The company spent £6.2bn on 3G spectrum 13 years ago, and borrowed to pay for it. Accounts show its UK operating company, Vodafone Limited, owes £6.3bn not to a bank, but to another group company.

Instead of being repayable in instalments, the entire loan will remain outstanding until 2021, when the 3G licences were originally due to expire, generating a hefty £300m a year in interest payments. Which means Vodafone Limited will have spent £6.3bn on interest by the end of the term – as much as it spent buying the spectrum in the first place.

Vodafone can get back from the taxman a quarter of the money paid in interest, and a quarter of the cash it originally spent on the spectrum. This means the government is in effect giving back to Vodafone half the money it spent on 3G spectrum.

Vodafone says its arrangements are in full accordance with UK law, that its loan reflects "good value", and that at no point does the money go offshore. It says the money passes through a series of UK companies and the loan was ultimately arranged with UK banks on "fully commercial terms".

Another business that will benefit from tax relief on money owed to sister companies is Three. The smallest and least profitable UK network, it has made one tax payment in the last three years but credits mean it has contributed less than £1m.

The network has been kept afloat by its parent, Hutchison Whampoa, the powerful Hong Kong conglomerate that owns ports and property around the world.

The accounts show that the UK business owes £1.3bn to Hutchison Westminster and Hutchison Lambeth, two sister companies based in the British Virgin Islands but taxable in Britain.

The debt is labelled in the accounts as for "royalties", and it carries interest. The UK business owes Lambeth and Westminster £132m in interest charges, up from £80m in 2010.

It is understood that these royalties are not for use of the brand but are instead a complicated transaction in which a portion of future UK income was sold and leased back to the operating company.

The structure is complex but the intention is simple: to build up Three's UK tax asset. This is the accumulated loss that can be used to reduce tax payments in future years, when Three starts turning a profit.

A spokesman for Three said the company was entitled, like any other British business, to offset historic losses against tax.

"If the government wants to stop this they should stop tax relief on any borrowing," says Sikka. "If you and I buy a house we don't get tax relief on our mortgage."

O2 pays the most tax of any mobile operator in Britain, and a spokeswoman says the company contributes significantly to the economy. It contributed £669m between 2009 and 2011, the most recent accounts show.

The reason O2 is able to report a profit and therefore pay tax is because in 2003, before smartphones came of age and made using the internet on a mobile network an everyday reality, it wrote down the book value of its 3G spectrum after concluding it had overpaid. Today it has less investment in that spectrum to claim against profits than its rivals.

But the dividends paid by O2 to its Spanish parent company Telefónica still dwarf its tax. Over three years, the UK business has exported £2.45bn in dividends. Dividends are not tax deductible, and therefore have no impact on a firm's ability to pay corporation tax.

Defending his company's tax record, Vodafone's chairman, Gerard Kleisterlee, told investors at its annual meeting that tax reliefs were "a cornerstone of UK taxation policy" and not a loophole.

"The government wants to stimulate investment so it allows companies to offset the interest of their debt against the profits when determining their corporate tax base," said Kleisterlee. "Those rules are intentional, long established and carefully considered. They reflect deliberate policy decisions by successive UK governments."

It is a policy that has certainly stimulated investment in British networks. However, when it comes to corporation tax, executives and shareholders have been free to reap the rewards of that investment long before the Treasury.

While the government collects money up front from spectrum auctions, it can no longer expect vast sums. This year's sale of the 4G airwaves designed to carry superfast internet connections, the biggest ever chunk of spectrum ever sold in a single auction, raised only £2.3bn. Networks spent £1bn less than the Treasury had budgeted.

Despite the price drop, of the four networks only O2 says it is likely to pay significant amounts of corporation tax in the near term.

The Conservative MP Charlie Elphicke, who last year launched a national campaign to ensure that multinationals paid their share, thinks the rules should be simplified.

Tax breaks could be scrapped and in return companies would pay a lower corporation tax rate – perhaps as little as 10%. "We need reform," says Elphicke, "with lower, simpler and stronger business taxes."