David Cameron's Conservatives are maintaining a strong lead over Labour.
A poll also suggests that Labour's prospects at the next general election could be almost identical under Home Secretary John Reid and Chancellor Gordon Brown.
But in both cases Labour would trail well behind the Tories.
The poll was commissioned for The Times and carried out by Populus.
Allies of the Prime Minister may be relieved to find that only 30% of Labour voters want him to stand down this year and 40% want him to stay until just before the next election.
Populus also found that half the public want Mr Blair to go this year, but at 51% this is only a two-point rise since July.
Asked how they would vote at the next election if Mr Brown took over, 33% of those interviewed said Labour.
This remains unchanged since July, but 42% still back the Tories under Mr Cameron and 16% the Liberal Democrats under Sir Menzies Campbell.
If Mr Reid took over as leader, Labour support would be virtually the same at 32%, with Tories on 40% and Lib Dems on 15%.
This suggests that if Mr Reid led Labour, the Conservative lead could be reduced to 7% from 9% under Mr Brown.
