Google’s attempt to counter criticism of its tax arrangements by agreeing to make a back payment of £130m in the UK unravelled after claims that the internet giant had effectively paid an annual rate of corporation tax of just 2.77% over the last decade.

Most British businesses currently pay corporation tax on 20% of their profits. But even after the extra payment, the internet giant is said to have paid just £200m in tax since 2005, on estimated profits in the UK of £7.2bn.

Professor Prem Sikka, a tax avoidance expert at the University of Essex, estimated that the company has avoided around £1.6bn in taxes over the decade, despite earning 10% of its global revenues in the UK. Sikka made the claim in response to a deal under which Google agreed to pay £130m in additional tax, on top of the £70m it has already paid on its profits in the UK since 2005.

Speaking at the World Economic Forum in Davos, the chancellor, George Osborne, celebrated the move as a “really positive step”.

“This is a major success of our tax policy,” he told reporters. “We’ve got Google to pay taxes and I think that is a huge step forward and addresses that perfectly legitimate public anger that large corporations have not been paying tax. I think it’s a really positive step … I think it’s a big step forward and a victory for the government.”

Google will now pay tax on revenues from UK advertisers, as well as its existing profits-based formula. Matt Brittin, Google’s president of business and operations for Europe, said the new tax arrangement “reflects the size and scope of our UK business”.

However, the shadow chancellor, John McDonnell, was quick to pour scorn on the “derisory” payment, arguing the public would be extremely sceptical about what he warned looked like a “sweetheart deal”.

McDonnell added he would demand details of the deal from Osborne in parliament on Monday and criticised HM Revenue & Customs for agreeing to recoup a “relatively small amount”.

He suggested the National Audit Office should examine the deal, and said: “It looks to me from all the independent analysis that this is relatively trivial in comparison with what should have been paid.”

Sikka, who is undertaking a review of HMRC for Labour, added that he believed the deal raised “more questions than answers”. He said: “We need to know how they came to this figure of £130m. The UK corporation tax rate in 2005 was 30% and is now 20%.

“We could do lots of averages but let us be generous and assume that the average rate for the period is 25%. That would mean that on its estimated £7.2bn UK profit Google should have paid corporation tax of £1.8bn. At best, it paid about £200m. That is an estimated shortfall of £1.6bn – lots of nurses and teachers, and probably bigger than the yield from the bedroom tax.

“Osborne will probably chicken out of explaining and say that the Treasury does not discuss individual tax payments but they have instigated this by talking about it, so that is out of the window.”

The Conservative MP Mark Garnier, a member of the Treasury select committee, also said the agreement represented a relatively small amount of money. “They are turning over billions a year and still paying relatively small amounts of tax,” he said.

Writing in the Observer, Margaret Hodge, the former chair of the Commons public accounts committee, who played a major part in shaming Google over its tax in recent years, said she believed that Google continued to be hypocritical in claiming “we do no evil”.

She said: “In the public’s eye, the issue of tax is quite simple and straightforward. The amount you pay is directly related to what you earn or to what profits you make.

“It is hard to believe that £13m [a year] tax payment on $6.4bn turnover is an adequate tax bill. It feels more like a PR deal designed to counter the reputational damage created by Google failing to pay a fair share of tax on the profits they make from their economic activity in the UK.”

Meg Hillier, the current chair of the committee, said she would demand that Google and tax officials explain the deal, which she said showed HMRC “admitting it pulled in too little tax from Google for nine out of 10 years”.

Google said: “The way multinational companies are taxed has been debated for many years and the international tax system is changing as a result. This settlement reflects that shift and is in line with recent OECD guidance.”

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