The system will be phased out as part of a massive review which will see the scrapping of vouchers, the introduction of identity cards, and a renewed drive to deal with the backlog of applications for asylum.
Mr Blunkett is dramatically overhauling his predecessor Jack Straw's failed asylum policy.
He said: 'I do not intend to tinker with the existing system, but to bring about radical and fundamental reform. Implementation of my policies will take time, but they will work in the interests of us all.'
The plans include a network of induction centres in areas where large numbers of refugees enter the country, instead of emergency bed-and-breakfast accommodation.
There will be reporting centres, so the government can keep track of refugees' movements, and a trial scheme of accommodation centres near major towns.
No planning permission has been granted for any of the accommodation centres.
A spokesman for Glasgow City Council, where a refugee was stabbed to death, said he was concerned about ghettoising refugees.
He added: 'Things have calmed down in Glasgow and overall we welcome these proposals, but accommodation centres could alienate refugees from communities.'
The government intends to speed up the appeals process and increase the number of decisions made each month from 4,000 to 6,000 within 12 months.
Kent CC leader Sandy Bruce-Lockhart (Con) said the plans were 'a step in the right direction'.
He added: 'We have been suggesting assessment centres and welcome these proposals. But centres like this are no good if the appeals process is not speeded up. The government needs to tackle the issue of repatriation when applications fail.'