It comes at a crucial time just before the Scottish and Welsh parliamentary elections and the local English elections in May and suggests Mr Blair's party now has the lowest level of support since the calamitous leadership of Michael Foot.
But the prime minister, who is expected to stand down as prime minister shortly after next month's voting, remained bullish.
"When you've been ten years in government and you've been the prime minister for ten years, people tend to hold pretty strong views about you one way or the other, sometimes the other," he told the BBC's Breakfast programme.
"The important thing for us is to concentrate on keeping the economy strong, making sure that we get the investment in the NHS and education, continuing the drive on antisocial behaviour.
"And obviously we've got a very challenging time in the health service, but on the other hand, you also see that the treatment for patients is improving the whole time."
Questioned as to whether he should have stepped down before the local elections, Mr Blair was adamant that he had made the right decision.
"In the end the important thing for me - I did after all say I would serve a full term - is to make sure that I just carry on with the job, get things done, and in the end people make a judgment about you at a later time."
It had been widely speculated that environment secretary David Miliband would fight chancellor Gordon Brown to take over as prime minister, but Mr Miliband has now ruled himself out of the competition.
The only other party members to have signalled their intention to challenge Mr Brown are both left-leaning backbench MPs not expected to pose the chancellor a significant threat - former environment minister Michael Meacher and John McDonnell.
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