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Margaret Hodge, chair of the public accounts committee, said major corporations should be stripped of their right to full privacy over their tax affairs.
She told the Independent new rules should be brought in forcing companies to make a full disclosure to MPs in closed sessions, which would allow their arrangements to be scrutinised.
Mrs Hodge told the newspaper: "We could have a committee of MPs overseeing them in private, the same way that the Intelligence and Security Committee operates. That has operated very effectively. There has never been a leak."
Google's executive chairman Eric Schmidt said the company pays "the mandatory amount" in tax and denied that a legalistic approach to paying taxes did not sit well with the firm's pledges on social responsibility.
He told BBC Radio 4's Start the Week: "I do not agree with this and the reason is that at least under American law we have a fiduciary responsibility to our shareholders to account for things properly.
"So if we were, for example, to just arbitrarily decide to pay a different tax rate than we were required to, a more favourable one for example to a particular country, how would we account for that?
"How would we file the necessary paperwork, what would be the legal consequences in other countries?
"Somehow these questions are ignored in the debate. We are very happy with whatever the countries all come to agreement on. We are not particularly upset about it."
He added: "Our position is very simple, taxes are not optional, we pay the mandatory amount."
Google boss Eric Schmidt said he was "perplexed" by the debate over the company's tax affairs.
The internet giant's executive chairman insisted it was up to the Government to change the law if it wanted more money from the firm after reports Google paid only £10 million in corporation tax in the UK between 2006 and 2011, despite revenues of £11.9 billion.
Mr Schmidt told BBC Radio 4's Start the Week: "What we are doing is legal. I'm rather perplexed by this debate, which has been going in the UK for quite some time because I view taxes as not optional.
"I view that you should pay the taxes that are legally required. It's not a debate. You pay the taxes.
"If the British system changes the tax laws then we will comply. If the taxes go up we will pay more, if they go down we will pay less. That is a political decision for the democracy that is the United Kingdom."
Labour leader Ed Miliband said it was "wrong" that Google had gone to "extraordinary lengths to avoid paying its taxes."
In a speech at Google's big tent event, he said: "I can’t be the only person here who feels disappointed that such a great company as Google...will be reduced to arguing that when it employs thousands of people in Britain...it’s fair that it should pay just a fraction of one per cent of that in tax.
"So when Google does great things for the world, I applaud you but when Eric Schmidt (Google's executive chairman) says, its current approach to tax is just 'capitalism', I disagree.
"And it's a shame Eric Schmidt isn't here to hear me say this direct: When Google goes to extraordinary lengths to avoid paying its taxes, I say it’s wrong."
Ed Miliband will today challenge Google on its tax affairs in Britain, using a speech at an event held by the corporation to say "Google shouldn't be going to extraordinary lengths to avoid paying its taxes."
Shadow business secretary Chuka Umunna told Daybreak:
"The problem is what we see [companies] do is artificially reduce their tax bill, and this is a serious issue because business and society, we're mutually dependent", he added, "if one factor in that relationship doesn't meet its obligations then the whole system can fall apart."
Last week Google was branded "devious," "calculating" and "unethical," as furious MPs stepped up pressure on the internet giant over its efforts to shelter its multi-billion profits from UK taxes.
The internet giant denied trying to "disguise" the way its business operated to minimise its tax bill in the UK.
Google UK boss Matt Brittin insisted he stood by evidence he gave last year that all the firm's advertising in Europe was sold through its offices in Ireland.
Committee chairman Margaret Hodge said his claims were contradicted by documentation MPs had seen and evidence from a "stream" of whistleblowers.
Mr Brittin said the evidence related to the period before he joined the company six and half years ago and that suggestions that Google was trying to "disguise" the way it operated were "just not true".
"I stand by what I said. I described very clearly how we operate," he said.
Labour leader Ed Miliband has condemned internet giant Google for their efforts to avoid paying tax in the UK. In a blog on The Huffington Post UK he wrote of the responsibility of new online companies to stand up for the values they appear to espouse: