The YouGov poll for The Daily Telegraph on Friday put Labour on 36% just ahead of the Conservatives on 35%, with both parties up one percentage point from a similar survey last week.
At the previous two elections in 1997 and 2001, Blair easily won triple-digit majorities.
The YouGov findings, which are broadly in keeping with other polls in giving Labour a narrow lead, would still mean Blair would be returned for a historic third term in power but with a reduced parliamentary majority, the newspaper said.
Analysts say the Conservatives would have to be significantly ahead in the public vote to oust Blair.
Britain's electoral map, which favours Labour's urban strongholds, means the Conservatives must now win a larger share of the vote than Labour to take power.
However, the poll found that a lack of trust in Blair and many of his ministers was the main issue that would be uppermost in the minds of those surveyed when they came to vote.
Blair's personal trust ratings slumped over the Iraq war and the subsequent failure to find any weapons of mass destruction
- the reason Blair gave for joining the conflict.
Thirty-five per cent rated a lack of trust as the most important factor ahead of traditional issues such as crime and health.