The Treasury is under pressure to urgently review rules allowing Vodafone to avoid paying tax on its massive £84bn windfall from selling its stake in the American mobile phone giant Verizon.

Public spending watchdogs claimed the UK-based phone company has a moral duty to hand over some of its gains to taxpayers. But there was no sign that the Chancellor George Osborne would change the law.

While UK taxpayers miss out, banks working for Verizon could earn as much as £80m in fees and Vodafone’s advisers could reap a £76m dividend, according to estimates by New York research group Freeman & Co, which exclude underwriting fees.

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In one of the biggest deals in corporate history, Vodafone confirmed last night that it is selling its 45 per cent holding in US firm Verizon Wireless to Verizon Communications. About £60bn will be returned to Vodafone shareholders, £24bn to those in Britain.

Vodafone says its US stake is owned by a holding company based in the Netherlands, and so will not be liable for tax in Britain. It will pay £3.2bn in tax in the United States.

Even if the US shareholding were held in the UK, the firm would not be liable to tax on its gains under rules on shares sell-offs introduced by the then Chancellor Gordon Brown in 2002.

Margaret Hodge, Labour chairman of the Public Accounts Committee (PAC), said: “We need assurances that HM Revenue & Customs (HMRC) have crawled over this deal and done its damnest to make sure taxpayers receive the highest amount of this sudden windfall. If there is a flaw in the legislation, Treasury ministers should look at it urgently.”

The PAC, which has attacked tax avoidance by companies such as Google, Amazon and Starbucks, also criticised an alleged “sweetheart deal” between Vodafone and HMRC which allowed Vodafone to forgo a reported £6.75bn of tax after its own takeover of Germany’s Mannesmann company in 2000. Dave Hartnett, the former HMRC boss, was accused by the MPs of letting Vodafone off the hook, which he and the company denied.

Ms Hodge’s committee may now investigate Vodafone’s US deal as part of an inquiry into tax reliefs. She said: “It is a British company with British customers. It takes advantage of services provided by the public purse and should pay its rightful dues. If Vodafone has, as it has done before, played the [tax] system, then it has an obligation to UK consumers to do the right thing.”

Lord Oakeshott of Seagrove Bay, the Liberal Democrats’ former Treasury spokesman, said: “Vodafone is right up there with Google and Amazon in the world tax dodgers’ league. What possible commercial justification is there for pretending that Newbury-based Vodafone made their investment in Verizon through Holland?

“They led HMRC a merry dance in the unlamented reign of Dave Hartnett - the new HMRC management and the Government must make every effort now to collect some tax at least on this profit.”

The Government refused to comment. But ministers are expected to stick with the “substantial shareholdings exemption”, which means firms to do not have to pay tax on profits from selling a 10 per cent stake or more in another company held for more than a year.

The Treasury believes the 2002 change boosts Britain’s competitiveness and encourages multinationals to be based in the UK. It thinks it more likely that decisions on sell-offs are taken for the right reasons rather than the wrong ones, such as limiting a tax bill.

Vodafone sources argued that the tens of billions could be paid to UK investors, a significant injection of cash into the economy, similar to the Bank of England’s quantitative easing programme, which could aid the fragile recovery. Investors would also have to pay tax on it.

Vodafone insists it pays the taxes due in every country in which it operates - about £2.3bn around the world in the 2011-12 financial year. “For every £4 we make in profit, we pay £1 in corporate taxes globally,” it said. Vodafone paid £1.25bn to settle a long-running legal dispute with HMRC over the Mannesmann takeover, but denied reports that the tax authorities demanded £8bn.