The chancellor is under huge pressure after admitting discs containing the personal details of 25 million people have gone missing in the post.
Mr Darling said a junior Revenue official had broken the rules
Alistair Darling has apologised for the "extremely serious failure", which has exposed all Child Benefit recipients to the threat of identity fraud.
The Tories said he needed to "get a grip" and show basic competence, the Lib Dems asked where "the buck stops".
The chairman of Revenue and Customs has quit. Police are looking for the discs.
In a Commons statement on Tuesday, Mr Darling said two discs, containing personal details of all families in the UK claiming child benefit, had gone missing in October.
CHILD BENEFIT HELPLINE
He blamed a junior official at HM Revenue and Customs' offices in Washington, Tyne and Wear, who he said had broken rules by downloading the data to a disc, then sending it - unrecorded - by courier to the National Audit Office in London for auditing.
The discs contained personal details including names, address, dates of birth, National Insurance numbers and, where relevant, bank details of 25 million people.
MISSING DATA INCLUDES...
National insurance number
Name, address and birth date
Names, sex and age of children
Bank/savings account details
The Metropolitan Police are now leading the search for the two password-protected discs, the Independent Police Complaints Commission, which oversees the HMRC, is investigating how the security breach happened.
In his statement, Mr Darling said details of 25 million people, 7.25m families were on the discs, which never turned up at the NAO.
He said he was first told about the breach on 10 November, but he had delayed the statement because banks and building societies had asked for time to prepare and make sure security procedures were in place.
He said the police had said that they have no reason to believe that the discs had found their way into the wrong hands, nor any evidence of it being used for "fraudulent purposes or criminal activity."
Mr Darling told MPs: "This is an extremely serious matter. HMRC has a responsibility towards the general public who entrust it with highly sensitive personal information. It has failed to meet the high standards that should be expected of it."
Available to the parents, normally mother, of every child in UK under 16
Older children in full-time education still eligible
Taken up by almost 100%
It amounts to £18.10 a week for a first-born child
For subsequent children - it amounts to £12.10 a week
He said he knew millions of people would be concerned and added: "I deeply regret this and apologise for the anxiety that will undoubtedly be caused."
It has emerged that the data had been sent on computer discs in the post three times this year. HMRC chairman Paul Gray has resigned.
Shadow chancellor George Osborne told MPs: "Half the country will be very anxious about the safety of their family and the security and the whole country will be wondering how on earth the government allowed this to happen."
He said the security protocols were "absolutely worthless" and suggested the breach should be the final blow to the government's controversial ID card scheme as ministers "simply cannot be trusted" with people's personal information.
"Never mind the lack of vision - just get a grip and deliver a basic level of competence," he said.
Meanwhile Liberal Democrat Acting Leader Vince Cable said Mr Gray, had resigned "as a matter of honour" and asked: "Where does the buck stop in this government?"
Later he told the BBC it was not a resigning matter for Mr Darling yet. "He seems to have acted promptly and properly in responding to the immediate emergency. I think what may emerge in the days and weeks to come is something more serious and his position may well become untenable," he added.
He said the department was "in crisis", owing to job cuts and failures of management supervision.
Customs and Excise was merged with the Inland Revenue in 2005, creating the biggest department in Whitehall. It was also ordered to reduce its 94,000 total staff by 25,000.
This latest breach follows others, including the loss of a disc containing the details of more than 15,000 Standard Life customers in November and the theft of a laptop holding hundreds of people's details in October.
Mark Serwotka, of the Public and Commercial Services union, told the BBC: "Are we creating the conditions in which mistakes like this can be made?
"And whilst Paul Gray, I think, has done the honourable thing today in resigning, it's the government which should ask itself, did they ask Paul Gray to do the impossible - deliver more and more, with less and less?"
The prime minister's official spokeswoman said Gordon Brown has "full confidence" in Mr Darling. She added that Mr Darling has not offered to resign.