Mr Osborne said millions will worry about their bank account security.
Shadow chancellor George Osborne said the HM Revenue and Customs error, which includes child benefit and bank details of 25m people, was "catastrophic".
"This is the third and most serious breach at HMRC," said Mr Osborne.
He accused Mr Darling of lurching "from one crisis to another" and of failing every family in the land.
He said the problems should mark the "final blow" for the government's identity card programme.
"They simply cannot be trusted with people's personal information," he said.
'Anxious' citizens
He spoke out after the chancellor revealed the child benefit details, contained on two discs, had been sent by HMRC to the National Audit Office, but never arrived.
"The prime minister says that the first duty of government is the protection of the citizen - and today the government is responsible for breaching that duty of protection to 25 million people," he said.
"Half the country will be very anxious about the safety of their family and the security of their bank accounts and will be wondering how on earth the government allowed this to happen."
Never mind the lack of vision just get a grip and deliver a basic level of competence
George Osborne
Shadow chancellor
Mr Osborne questioned why it had taken the chancellor four days to contact the police after finding out about the "fiasco".
He asked when the prime minister was told - to which Mr Darling replied: "Within half an hour of me being told."
And he asked what the point was of the Commons passing laws to protect the privacy of personal information "if those laws aren't enforced at the heart of government".
In a personal attack on Mr Darling, he declared: "Since you came to office less than six months ago you have lurched from one crisis to another.
"Now your department has compromised the security and safety of every family in the land.
"This autumn the prime minister said he had shown this government could be competent and how he needed to set out his vision.
"There are 25 million people whose personal details have been lost by this government.
"Never mind the lack of vision just get a grip and deliver a basic level of competence."
'Extreme regret'
Mr Darling said the problem was "inexcusable". "HMRC has well laid down procedures and there was no excuse for breaching those," he said.
"It's a matter of extreme regret that so many people are going to be caused anxiety."
The chancellor defended the government's plans to introduce ID cards. He said that without the protection of the scheme, information was more vulnerable than it should be.
"This is a deeply regrettable incident - it should never have happened," he added.
Alistair Darling 
British Chancellor of the Exchequer Alistair Darling announced to a shocked House of Commons today that two password-protected — but not encrypted — computer disks containing the entire Child Benefit database have been lost in transit between the offices of Her Majesty's Revenue and Customs (HMRC) in Washington, Tyne & Wear and the National Audit Office (NAO) in London, in what has been described as "one of the world’s biggest ID protection failures".

The database contains details of all families in the UK who receive Child Benefit — all families with children up to 16 years of age, plus those with children up to 20 years old if they are in full-time education or training — estimated to contain 25 million individuals in 7.25 million families. Among other items of information, the database contains names, addresses, dates of birth, child benefit and National Insurance numbers, and where appropriate, bank or building society account details.

The discs were created by a junior official at the HMRC in response to a request for information by the NAO, and were sent unregistered and unrecorded on 18 October using the courier company TNT — which operates the HMRC's internal mail system. When it was found that the discs had not arrived for audit at the NAO, a further copy of this data was made and sent — this time by registered mail — and this package did arrive. HMRC were not informed that the original discs had been lost until 8 November, and Darling himself was informed on 10 November.

The violation of data protection laws involved in the creation of the discs has led to strong attacks on the government's competence to establish the proposed National Identity Register, when all UK residents will have an identity card. Conservative Shadow Chancellor George Osborne described the loss of data as "catastrophic" and said "They the government simply cannot be trusted with people's personal information".

The Chairman of HMRC, Paul Gray, has resigned over the affair, and critics are calling for Darling to do likewise.

This is the third data embarrassment for HMRC in recent weeks — earlier this month it was reported that the details of over 15,000 Standard Life customers had been put on disk, and then lost en route from HMRC in Newcastle to Standard Life in Edinburgh — and last month a laptop containing the data of 400 people with high-value ISAs was stolen from the boot of a car belonging to a HMRC official who had been carrying out a routine audit.