Brown remains front-runner to succeed Blair
Blair was last week forced to publicly announce that he will step down within a year, after a rebellion within his own government over his leadership.
Of the 1,519 people surveyed by YouGov, 28 percent said they felt Brown would make the best prime minister of a list of Labour Party MPs. Home Secretary John Reid came second with 15 percent, and Education Secretary Alan Johnson was backed by seven percent.
Some 44 percent, however, said they did not know, indicating the race is still open.
Labour also remained behind the main opposition Conservative Party, which was supported by 38 percent of the poll's respondents, compared to Labour's 31 percent. The smaller opposition Liberal Democrats polled at 18 percent.
Brown was only backed by 34 percent of those surveyed when asked who would make the better prime minister -- Brown, or David Cameron, the leader of the Conservatives. 43 percent backed Cameron.
Some 53 percent agreed that Brown has done a good job running Britain's economy in his nine years as chancellor, with 31 percent disagreeing.
The chancellor was accused, in the aftermath of the rebellion against Blair, of orchestrating the events, which saw eight junior members of the government resign after a letter was submitted to Blair demanding he stand aside.
About 51 percent of the respondents agreed that Brown had played an active role "in a plot to force Tony Blair to resign as prime minister". Brown has denied any involvement in the letter or the resignations.