Blair, the only leader of the Labour Party to win back-to-back general elections, has lost a significant amount of trust among the electorate, says a Mori poll published for the British newspaper Financial Times.
A total of 28% said they had never trusted him, while 38% said they had not trusted him since the start of the war that lead to the occupation of Iraq by US and British forces.
Elsewhere, 30% said they "strongly agree" that Blair was “losing his grip” while 33% “tend to agree”.
Only 31% said they were satisfied with Blair's performance as prime minister, against 61% who were not.
Mori interviewed 1002 adults by telephone between 20-22 June.
Loss of popularity
Blair has come under fierce criticism in recent weeks over his handling of the Iraq war.
A poll last month showed that the majority of British voters believe Britain and the United States deliberately exaggerated evidence that Iraq had weapons of mass destruction (WMD) in order to win support for going to war.
A parliamentary foreign affairs committee is currently investigating claims that Britain embellished intelligence on Iraq's WMD.
Blair’s aid – Alistair Campbell – admitted that a twelve year old post-graduate thesis presented as up-to-date intelligence on Iraq was “a mistake”.