Although the public remains broadly content with the Government and welcomes the extra money it has pumped into health and education, the people are increasingly worried about the economy.
The survey suggests the Government's standing would suffer even if a slowdown in Britain were caused by the global crisis.
The survey was carried out by Philip Gould, Mr Blair's polling adviser, and presented to the Cabinet at a strategy session at Chequers in the run-up to last week's Labour conference.
Mr Gould's poll has reopened a debate in the Cabinet about Mr Blair's style of government. Some ministers want him to relax the iron discipline he seeks to impose on his Cabinet, MPs and party as a response to criticism that his regime is run by a tiny inner circle of "control freaks".
One said: "People like most of what we are doing, but they don't like our style. There is sometimes a harshness about us; we should relax a bit and not look so preoccupied with getting our own way."
Mr Blair, whose personal ratings have dropped recently from the remarkably high level he has maintained since last year's general election, believes privately that allegations of "cronyism" have harmed the Government.
It is understood that he regarded the "lobbygate" affair, involving Derek Draper, a former frontbench aide-turned-lobbyist, as much more damaging than last year's row over tobacco sponsorship.
Bernie Ecclestone, the Formula One boss, persuaded Mr Blair last year to water down the Government's policy on tobacco sponsorship after donating pounds 1m million to the Labour Party.
Mr Draper claimed the country was run by only 17 people close to Mr Blair, including several backroom aides who enjoyed more power than some members of the Cabinet.
When he took office, Mr Blair told his ministers they were not in their jobs to enjoy "the trappings of power" and that the people must be their masters.
Yesterday Downing Street sources played down the poll findings, saying the Government was still seen as much less arrogant than the previous Tory administration.
"It was highlighting a potential problem which affects all governments, and warning us not to let this damage us as it did the Tories, " said one aide. "People do not think that Tony Blair is arrogant."
Mr Blair's advisers believe the best antidote to such criticism is for the Government to deliver its promises to improve public services and to convince people it is "on their side".
However, the poll findings will encourage the Tories to pursue their claims that the Government is run by "Tony's cronies".
Accusations that "power has gone to their heads" should form one line of attack on ministers during the Tory conference in Bournemouth this week.Reuse content