In an opinion poll in Wednesday's Daily Telegraph newspaper, just 26 percent of respondents said they were satisfied with Mr Blair's performance - one percent down from where Harold Wilson stood in May 1968 after a devaluation of pound sterling.
The survey also indicated that support for the main opposition Conservatives is running at 37 percent, against 31 percent for Labour and 17 percent for the smaller Liberal Democrats.
Despite a rash of scandals in his nine-year-old government, Mr Blair refused calls on Monday to name a precise date when he will stand down in favour of Chancellor of the Exchequer Gordon Brown.
But he signalled that would give his successor "ample time" to settle into Downing Street before the next general election, which must be held by May 2010 - language that some analysts interpreted as his intention to go in mid-2007.
YouGov's findings for the Daily Telegraph, a staunch editorial supporter of the Conservatives, reinforced an opinion poll in the more Labour-friendly Times newspaper on Tuesday which put Labour at its lowest ebb since 1992.
Some 65 percent of respondents said they expected Labour to lose the next parliamentary election, with the main opposition Conservatives enjoying a lead of eight points and the smaller Liberal Democrats on 20 percent.
Brown turns the screw
Meanwhile, his heir apparent Mr Brown appeared to turn the screw, warning against a repeat of Margaret Thatcher's "undignified" exit from the leadership in 1990.
In an interview with GMTV on Tuesday, Mr Brown said: "Tony said that he is going to be doing it in a stable and orderly way - that means that he is going to be talking not just to me but to senior colleagues about it.
"Remember when Mrs (Margaret) Thatcher left, it was unstable, it was disorderly and it was undignified," he added.
"I think we will prove to the world that we can do these things in an orderly, dignified and sensible and proper way, and do it in a way that is unifying as well as unified."
His allusion to Mrs Thatcher's ejection from office after senior colleagues withdrew their backing could be an implicit warning that Mr Blair could face the same fate if he tries to stay on.
Five months after Labour swept to power in May 1997, Mr Blair's satisfaction rating reached 83 percent - and despite the unpopular Iraq war he was able to lead Labour to an unprecedented third straight term a year ago.
But since then his government has been dragged down by a string of highly embarrassing blunders.
The latest include the Home Office's failure to consider hundreds of foreign convicts for deportation following their release from jail as well as a sex scandal involving Blair's deputy John Prescott.
The poor results in the municipal council elections in England that followed the scandals prompted Blair to sack his home secretary Charles Clarke, demote his foreign secretary, take powers off Prescott and juggle other key top posts.
YouGov questioned 1,910 people online on Monday and Tuesday.
A BBC radio survey of 104 Labour backbenchers found 52 who believed Mr Blair should stand down within a year.