A Gallup poll for the Daily Telegraph gives Mr Blair an 82 per cent popularity rating - 41 percentage points ahead of Margaret Thatcher at a similar stage of her leadership in 1979; 16 points ahead of Clement Attlee, who won the Labour landslide victory of 1945; and 22 points ahead of Harold Wilson.
Public backing for the new prime minister is now so great that 53 per cent of those replying to the Gallup survey claimed that they had voted Labour on 1 May - compared with only 43.2 per cent who actually did so.
Only 2 per cent of those interviewed thought that the performance of the new Labour government was poor, compared with 51 per cent who thought it was good, 13 per cent, excellent, and 31 per cent fair.
Two-thirds of those replying to the survey thought it had been a good idea for the Prime Minister to meet Baroness Thatcher for talks before last month's Noordweijk summit, in the Netherlands.
In all, 78 per cent of all those surveyed, and 57 per cent of Tory voters, thought Labour had so far been both honest and trustworthy.
But Mr Blair yesterday reminded the Cabinet, in a stock-taking exercise after five weeks in office, that ministers must "never lose sight of the big picture, never lose sight of addressing the people's priorities, that we were elected on a manifesto and that is what we are here to implement".
He said it was "absolutely essential that you don't get so busy governing you stop communicating".
A spokesman said: "The main thrust of what the Prime Minister was saying was that we have had five weeks, we have done a lot. There is a new mood of optimism out there and the important thing is we are being seen to implement what we have said we are going to do."
The Parliamentary Labour Party last night scored a significant coup for women members, who took five of the six places on a key committee that will liaise with the new government.
The top five women were: Jean Corston, Bristol East; Sylvia Heal, Halesowen and Rowley Regis; Ann Clwyd; Cynon Valley; Charlotte Atkins, the new MP for Staffordshire Moorlands; and Llin Golding, Newcastle-under-Lyme.
The lone male elected was Chris Mullin, the campaigning member for Sunderland South.Reuse content