Chancellor Alistair Darling is standing by his version of events of how discs containing the personal details of 25 million people went missing.
Police are continuing to search for the discs at HMRC offices
The Treasury said there was nothing in e-mails released on Thursday to contradict the chancellor's account.
The e-mails suggest a senior manager was involved - something not mentioned in Mr Darling's statement to MPs.
It comes as opinion polls suggest the data loss crisis has badly dented public confidence in the government.
A Populus poll for The Times suggests those backing Labour's ability to handle economic problems has been more than halved to 28%, with just a quarter deeming Prime Minister Gordon Brown's administration "competent and capable".
A YouGov poll for Channel 4 News gives the Conservatives a nine-point overall lead, its strongest position for 15 years, just weeks after Labour enjoyed an 11-point advantage in the same poll.
YouGov consulted 1,600 adults online on Thursday and Friday, with the results weighted to be representative of the population and Populus talked to 1,000 adults.
The government has been under fire since it was revealed two discs went missing in transit between HM Revenue and Customs' office in Tyne and Wear, and the National Audit Office in London.
On Tuesday, Mr Darling told MPs "junior officials" at the HMRC office had broken data protection rules by downloading the entire Child Benefit database - including millions of bank account details - onto two discs and putting them in the internal mail, where they were lost.
The Conservatives have blamed wider, "systemic" problems at HMRC, which had been under pressure to save cash.
On Thursday, the National Audit Office released e-mail exchanges, from March and October this year, in a bid to prove that senior officials did not sanction the downloading of sensitive data.
The e-mails showed the NAO had only asked the HMRC to send limited details from its database - stripping out information such as bank account numbers.
A covering letter confirmed a senior HMRC manager was copied in to another e-mail rejecting the request to remove the data as this would involve additional costs.
But the letter, by NAO assistant auditor general Caroline Mawhood, said there was "no evidence" the senior manager - the Process Owner for Child Benefit - "made the decision to release the data".
The e-mails also revealed that the NAO explicitly urged HMRC to ensure that the data was delivered "as safely as possible due to their content".
Shadow chancellor George Osborne said the e-mails raised "some very, very serious questions now about the version of events that (the chancellor) gave earlier in the week where he implied it was just some lowly junior official sitting by themselves at a computer.
Liberal Democrat acting leader Vince Cable accused the government of putting "minor cost-cutting" ahead of security.
Chairman of the Commons Public Accounts Committee, Conservative MP Edward Leigh, demanded to know why the senior HMRC manager concerned failed to halt the release of the data on security grounds.
But the Treasury insisted there was nothing in the e-mails that was inconsistent with Mr Darling's statement.
"While we still only have a partial picture, these matters are being investigated and we cannot pre-empt the outcome of this investigation," a spokesman said.
The briefing notes produced for the chancellor ahead of his statement, also released on Thursday, did not mention a senior official.
MISSING DATA INCLUDES
National insurance number
Name, address and birth date
Names, sex and age of children
Bank/savings account details
BBC Political Editor Nick Robinson said: "I am told that when he spoke to the Commons the chancellor had not seen the e-mails and had not been told of the potential involvement of a senior official."
He added: "The suggestion that a single 23-year-old on low pay at the Child Benefit Centre in Washington is solely responsible for this saga may suit certain people - including the managements of the NAO and HMRC who have clearly clashed in their accounts of this affair - but it beggars belief."
In a separate development, the government is seeking to reassure people that their personal details have not fallen into criminal hands.
In a letter being sent to seven million families, HMRC apologises for losing the data but says it is "likely to still be on government property".
It says police are continuing to search for the discs but "there is no evidence that it is in the possession of anyone else".
The Metropolitan Police refused to comment on the claim that the discs were probably still on government property.
A Met spokesman said they were continuing to search the HMRC's Waterview Park offices in Washington, Tyne and Wear, and the NAO offices in London.
Her Majesty's Revenue and Customs has set up a Child Benefit Helpline on 0845 302 1444 for customers who want more details.
LOST CDS - SEQUENCE OF EVENTS
18 October - Junior official from HMRC in Washington, Tyne and Wear, sends two CDs containing password-protected records to audit office in London through courier TNT, neither recorded nor registered
24 October - When package fails to arrive, second one is sent by registered post and arrives safely
3 November - Senior managers are told first package has been lost
10 November - Prime minister and other ministers are informed
12 November - HMRC tell ministers CDs will probably be found
14 November - When HMRC searches fail, Metropolitan Police are called in
15 November- Richard Thomas, Information Commissioner, says remedial action must be taken before public is informed
20 November - HMRC Chairman Paul Gray resigns; Chancellor Alistair Darling makes announcement to House of Commons
21 November - Prime Minister Gordon Brown apologises and orders security checks
22 November - E-mails show officials were concerned about cost and security of data