There is no record of any Government minister being informed by HM Revenue and Customs about alleged wrong-doing by employees of HSBC in relation to its Swiss banking arm, Downing Street has said.

As controversy raged over allegations that the Geneva subsidiary was used by thousands of customers for large-scale tax evasion, Labour demanded to know whether former chairman and chief executive Lord Green was asked how much he knew at the time of his appointment as trade minister in David Cameron's Government.

And the party's Treasury spokeswoman Shabana Mahmood called on Chancellor George Osborne to say whether tax authorities - who have so far pursued only one criminal case in relation to the HSBC files - were taking a "selective prosecution policy" towards the 6,000 cases passed to them by France in 2010.

A Downing Street spokeswoman initially said that neither Lord Green - who served as a coalition minister from 2011 to 2013 - nor any other member of the Government had "any knowledge that HSBC may have been involved in wrongdoing" in relation to its Swiss operation until the allegations were reported in the media over the past few days.

But she later acknowledged that she could not rule out ministers having read media reports about the scandal in the years since a huge cache of files relating to secret Swiss accounts was first passed to French authorities by an IT worker in 2007.

"We have no record that any Government minister was made aware by HMRC officials that HSBC employees may have been involved in wrong-doing relating to its Swiss banking arm prior to the media reports in recent days," the Number 10 spokeswoman told a regular Westminster press briefing.

"There is a distinction between illegal wrong-doing by HMRC employees and information suggesting that individual clients at HMRC were using Swiss bank accounts and were being investigated, which has been in the public domain for a while."

She said that when French authorities passed files to HMRC in 2010, they imposed restrictions on how the material could be used.

The files have already sparked criminal probes in several countries, and in 2011 then HMRC boss Dave Hartnett told a parliamentary inquiry that "the whole nation probably knows that our Department has a disc from the Swiss - from the Geneva branch of a major UK bank - with 6,000 names, all ripe for investigation."

Details of 30,000 accounts holding almost £78 billion of assets recorded in the files were recently obtained by a French newspaper and analysed by a team of investigative journalists, including reporters from The Guardian and the BBC's Panorama.

Shadow chancellor Ed Balls said the Government was "in an utter state of confusion" over the HSBC files.

While accepting it would not be usual for ministers to be informed about individuals' tax affairs, he told BBC Radio 4's World at One: "If you have something on this scale and of this seriousness, in my experience of many years in the Treasury, it beggars belief that HMRC would not have told the Chancellor of this systemic problem happening in one bank, but affecting very, very many individuals."

Financial Secretary to the Treasury David Gauke yesterday told the House of Commons there was no evidence to suggest that Lord Green was "involved or complicit with tax evasion activities", while Mr Cameron defended him as an "excellent trade minister" .

But Ms Mahmood told Mr Osborne in her letter: "Given that, as the Financial Secretary said yesterday, the Government was made aware of allegations of wrongdoing against HSBC in May 2010, eight months before Mr Green's appointment to government, failure to ask probing questions would have to be seen as wilfully negligent.

"As chairman of the bank, Mr Green would either have been aware of malpractice or, if not, surely questions would arise as to why not and his fitness for such a senior government post of trade minister.

"Can you provide details of the due diligence carried out by the Government in advance of Lord Green's appointment concerning allegations against HSBC and Lord Green's role in relation to them?

"I hope you agree it is essential that we now hear from Lord Green himself about what assurances he gave on his appointment to be a member of the government and what he knew about the activities at his bank, so will you encourage him to do so urgently?"

Ms Mahmood quoted a HMRC official who was reported to have said in 2012 that taxmen were taking a "selective prosecution policy" towards cases related to the HSBC files. And she noted that senior HMRC official Edward Troup told the House of Commons Public Accounts Committee later that year that, while only one criminal case had so far been brought, another dozen were "in train".

She said: "There have been none since. It seems HMRC took a deliberate strategy to minimise rather than pursue prosecutions."

HMRC said it had "systematically worked through" all the data provided and recouped £135 million in tax, interest and penalties from those seeking to get out of paying tax by hiding their assets in Switzerland

"The decision to prosecute is made by the Crown Prosecution Service based on the facts," said the HMRC.

Business Minister Matt Hancock said it was "entirely appropriate" that ministers were not informed about the allegations concerning HSBC, even though it was Britain's biggest bank.

"Politicians don't know and aren't told about the individual tax affairs of individual people. Britain's biggest bank is also a private company and so it is entirely appropriate," he told BBC Radio 4's World At One.

Asked about reports last year that the US authorities had fined HSBC millions of dollars to resolve charges that its Swiss private banking unit illegally offered services to US clients without being properly registered, he said: "I personally didn't know more than was in the public domain."