Almost two thirds of British people support indefinite detention of foreign terror suspects without charge, a poll for the BBC indicates.
Mr Blunkett wants to prevent more terror suspects from being released
A similar figure support extending such restraints to British terror suspects, the ICM poll suggests.
The poll was taken following last week's decision to release a suspect, held without charge for two years.
Of the 510 people questioned, 58% supported detaining people suspected of associating with terror suspects.
Home Secretary David Blunkett has criticised the decision by the Special Immigration Appeal Commission to release "G", an Algerian man with alleged links to Al-Qaeda, on bail on mental health grounds.
He said the ruling was "extraordinary", and added that others might term it "bonkers".
Of those polled, 69% supported the idea of police having wider powers to stop and search.
However, asked if police should have greater power to eavesdrop on phone conversations or read emails, support dropped to 46%.
Where such eavesdropping evidence did exist, 63% of respondents said it should be admissible in court.
On the question of lowering the standard of proof to make it easier to secure a conviction in terror cases, opinion was split - 49% in favour and 45% were against.
The BBC's Mark Easton said this was not the first time certain civil liberties had been suspended.
"World War II saw UK citizens interned on British soil, and in Northern Ireland the right to jury trial remains suspended for some crime cases.
" Now the British public, it seems, believes the 'war on terror' also justifies the suspension of certain traditional civil rights."
Professor Conor Gearty, from the London School of Economics director of the Centre for the study of Human Rights, said: "People perceive that there is a serious security problem facing them today and ministers who are elected are all terrified of having to explain a massive atrocity."
Sir Nigel Rodley, professor of law at University of Essex and a member of the United Nations Human Rights Committee, described the poll results as "predictable".
"Obviously people are going to be in favour of measures that protect them from dangers," he told BBC Radio 4's Today programme.
"We have to be very careful not to ignore the dangers."
However, he added a note of caution, saying: "There is a very heavy burden on authorities to do something about it, but that doesn't mean that every measure that is thrown out is necessarily going to be good."
He said it was yet to be shown that existing measures were effective.