Up to 15,000 refugee families could get permission to live and work in the UK as part of Britain's biggest-ever asylum amnesty, it has been announced.
Mr Blunkett said the decision was a 'one off'
Home Secretary David Blunkett said the majority of those being granted leave to remain - about 30,000, including children - were currently subsisting on benefits.
Granting permission to work would lift a burden from taxpayers.
But Conservative home affairs spokesman Oliver Letwin said the move sent out the wrong signal and people would be "appalled".
"It cannot be right, while the system still remains in total chaos,
to send out a signal that 15,000 people who have failed to establish a claim
will be allowed to remain indefinitely.
"This amnesty is a result of the government's failure to deport failed asylum seekers in significant numbers.
"This decision will make Britain a magnet for asylum seekers who now know
that even if their cases are rejected they could be allowed to stay."
Liberal Democrat home affairs spokesman Mark Oaten said: "This is a welcome
decision, but the Home Office should never have allowed the backlog to occur."
Mr Blunkett said the families involved - from Kosovo, the Federal Republic of Yugoslavia and Turkey - had sought asylum in the UK more than three years ago.
The move comes ahead of the final stages of a government shake-up of the asylum system.
Officials say the reforms - which will end all future support for families refused asylum - will ensure the system is not open to abuse or delays.
So-called "hard case" applicants will only be given benefits if they agree to comply with the removal process once it becomes possible for them to go home.
Mr Blunkett said: "Granting this group indefinite leave to remain and enabling them to work is the most cost-effective way of dealing with the situation and will save taxpayer's money on support and legal aid.
David Blunkett said tough new measures are on their way
"These are difficult decisions but I do not believe it is the best use of taxpayer's money to take these expensive longstanding individual appeals through the courts.
"I want to ensure our relentless focus is on steadily increasing the proportion of failed asylum seekers removed from now on."
The home secretary added that his decision was a "one-off exercise" that would end the uncertainty suffered by many families.
Official figures show that the taxpayer is currently supporting 12,000 families who applied for asylum prior to October 2000.
The Home Office said that moving 1,000 of them off benefits "will save £15m in support costs in addition to any potential savings on legal aid".
Up to 3,000 families who are self-supporting could also qualify to stay in the UK.
A spokesman said: "The families will be given the immigration status of "indefinite leave to remain" in the UK which means they are able to live and work here without restrictions."
The decision to end support for families denied asylum was intended to remove the "incentive" for people to delay being removed from the UK.
It would save money in support and legal costs, the spokesman added.
Those measures were welcomed by the Tories.
"I welcome measures designed to
improve the lamentably ineffective removal system for those who have been unable
to demonstrate any claim to asylum," said Mr Letwin.
For the Lib Dems, Mr Oaten said the government should make every effort in the future to make sure the children were not left in limbo.
Mr Letwin attacked the government's decision
Margaret Lally, of the Refugee Council, welcomed the government's decision, adding that without it, the people concerned would not have been dealt with until 2008.
Sandy Buchan, Refugee Action's chief executive, welcomed the "sensible decision", but said it was "harsh" to end support for families denied asylum.
MigrationwatchUK chairman, Sir Andrew Green said the amnesty was not so much "clearing the decks" as "abandoning" ship.
"The message to asylum seekers is clear - 'remain here illegally for long
enough and we will give you permission to stay'."