The ICM poll published on Monday in The Guardian newspaper showed that 73% of respondents backed the trade-off, with only 17% rejecting it outright.
The results suggest the British public largely backs a range of anti-terrorism measures proposed by Prime Minister Tony Blair's government, including a new offence of inciting terrorism and deporting radical clerics who glorify acts of violence.
ICM interviewed 1006 adults by telephone between 12-14 August. The margin of error was plus or minus three percentage points.
Since 7 July when four bombers killed 52 commuters along with themselves, and the failed attacks two weeks later, Blair's government has been trying to build support among political opponents and Muslim leaders for new anti-terrorism legislation.
The majority of polled Britons
support a deportation policy
Some of the proposals, including barring radical Islamic clerics from entering Britain, closing down mosques linked to extremism, banning certain Islamic groups and, if necessary, amending human rights laws, have concerned civil rights campaigners and Muslim leaders.
But according to the poll, the public appears to support the changes. Sixty-two per cent of respondents backed deporting foreign nationals who spread radical Islamist views, even if they were returned to countries which use torture.
Sixty-eight per cent of interviewees also backed extending from two weeks to three months the length of time a suspected terrorist can be held without charge, as requested by British police chiefs.
The poll also shows that Blair's popularity rating has risen.
He is now narrowly into positive figures, with 47% of respondents satisfied with his performance as prime minister, and 45%, not.
In a similar poll conducted in January, 38% were satisfied and 50% were not.