Mr Blair concedes his Iraq policy has had an impact
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Tony Blair's rating among voters has plummeted since last year's local elections, according to a poll conducted by ICM for the BBC.
Liberal Democrat Charles Kennedy is seen as the most trustworthy of the three main party leaders
Mr Blair is seen as less trustworthy - but he is still rated more highly on this measure than Conservative leader Michael Howard.
The survey comes within hours of polls closing on 'Super Thursday'.
They include local elections in England and Wales, the London mayoral and assembly votes and the poll for the European Parliament.
The elections are seen as the biggest test of public opinion since the 2001 general election.
Labour is widely expected to suffer losses in council elections and Mr Blair has already conceded that his decision to take Britain to war with Iraq cast a shadow over the polls.
Competent?
But Mr Howard's Conservatives could also have a disappointing night if the UK Independence Party, which wants Britain out of the EU, enjoys a surge in support.
The ICM poll suggests 47% of those asked thought the premier is respected abroad - down from 63% in 2003.
Last year 51% thought Mr Blair trustworthy, compared with 39% now.
Just 33% think he is in touch with ordinary people - a fall from 42%.
But of those questioned 63% regard the prime minister as competent - down just 5%.
Economy
Mr Howard's is regarded as competent by 52%, trustworthy by 33% and in touch with ordinary people by 29%.
According to the poll, Mr Kennedy is seen as competent by 53%, trustworthy by 58% and in touch with ordinary people by 53%.
Labour is more widely trusted to run the economy than the other parties, the survey indicates.
Labour is seen as having the best leadership team.
For its poll, ICM questioned 1,016 adults between 4 and 6 June.