George Osborne faces further questions over the Google tax deal, with calls for greater transparency about how the £130 million settlement was reached.
London Mayor Boris Johnson called for "clarity" on where Google's profits are made and senior Tory backbencher David Davis said the amount of back tax the firm has agreed to pay was a "very small number".
HM Revenue and Customs (HMRC) has defended the deal, with a senior official insisting that it was collecting the "full tax due in law".
But shadow chancellor John McDonnell wrote to Mr Osborne demanding details of the settlement and questioning whether he or anyone else from his team in Number 11 was involved in the arrangement.
He asked when Mr Osborne was first aware of the deal and whether he or a ministerial colleague personally signed it off.
Mr McDonnell also asked whether Number 10 was involved in discussions of the deal before it was announced.
Claims that the settlement covering 10 years from 2005 amounted to a 3% tax rate have been rejected by officials and ministers, but Mr McDonnell asked: "What is HMRC's understanding of the effective tax rate faced by Google over the past 10 years as a result of this settlement?"
Mr McDonnell also raised a Times report that HMRC had never challenged Google's assertion that it did not have a "permanent establishment" in the UK.
"Such a claim is obviously critical to the entire tax issue," he said.
He told Mr Osborne: "When times are tough it is more important than ever that everyone pays – and is seen to pay – their fair share. I know that many are concerned about the tax treatment of large companies and it is important for public trust that HMRC is fair and transparent in its dealings with such companies."
Mr McDonnell said there appeared to be "disagreement about the significance of the deal at the highest levels of Government", with Downing Street not repeating Mr Osborne's claims of "victory" and a "major success".
But Downing Street rejected the suggestion that Number 10 was distancing itself from the Chancellor and insisted no ministers were involved in the arrangement between HMRC and Google.
"The Prime Minister and the Chancellor are of the same mind on this," a Downing Street spokesman said. "This was a good deal."
Mr Johnson told Sky News that people wanted "clarity on where their profits are being made and an agreement on how much they should be paying".
Former Tory leadership contender Mr Davis, vice chairman of the all-party parliamentary group on tax responsibility, said firms should not be covered by the same tax confidentiality rules as individuals and the arrangement should be put "entirely in the open".
"Otherwise people are always going to be saying 'this is too small a number'," he told Sky. "It is a very small number."
Jim Harra, HMRC's business tax director general, told BBC Radio 4's World at One: "We only accept the full amount of tax, interest and penalties that is due, otherwise if we can't reach an agreement on that amount we will go to tribunal. We certainly don't apply any rate of tax other than the statutory rate that Parliament has published."
Google has taken advantage of lower tax rates in Ireland to base parts of its business there, and Mr Harra acknowledged "multinationals do have capabilities and resources to structure themselves in the most tax-efficient ways, from their point of view" but "we have some rules that protect us from avoidance".
Responding to the claims in The Times that a French investigation was seeking a settlement three-times that agreed by HMRC, he said: "We will have to wait and see what the outcome of any inquiry in France is, there has certainly been no disclosure that there has been any outcome.
"I am satisfied that we have carried out a thorough investigation and we have collected the amount of tax that is due under the law and I am quite happy to be held to account for what we have done."