Asked if it was "now time for Tony Blair to resign and hand over to someone else", 51 percent of respondents agreed, with only 35 percent giving a definite no, the poll for The Independent newspaper showed.
The findings end a miserable week for the prime minister, which saw him forced to order an investigation into whether there were failures of intelligence ahead of the war.
Separately, 54 percent thought Blair lied to Britain about the threat posed by Iraq's alleged weapons of mass destruction ahead of the campaign last year to remove Saddam Hussein (news - web sites).
Blair faces mounting political pressure over the fact that no stocks of chemical or biological weapons have been found in Iraq, nine months after the fall of Baghdad.
Before the war, the prime minister insisted to a sceptical nation that it was correct to join the US-led conflict because Saddam's arsenal of illegal weapons posed an immediate threat to the West.
The telephone poll of 1,003 people showed that the main opposition Conservative Party has benefited from the backlash against Blair, with 36 percent of people backing them against 35 percent for Blair's Labour Party.
On Tuesday Blair announced that a former head of the civil service would lead an inquiry into pre-war information about Iraq's weapons of mass destruction.
However Saturday's poll showed that 68 percent of people believe the probe will end up being a "whitewash".
Similar charges were levelled against a report by judge Lord Brian Hutton, who at the end of last month exonerated Blair's government of deliberately exaggerating a dossier on Iraq's weapons.
Hutton instead lambasted the BBC for reporting that a claim Iraq could unleash chemical or biological weapons within 45 minutes had been inserted by ministers even though they knew it was wrong.
However even this issue has returned to haunt Blair.
On Wednesday, Blair was ridiculed by critics after admitting that when the 45-minute claim was made, he had no idea whether it referred only to short-range "battlefield" weapons or also to missile-launched devices.
