Ministers are hoping that the recent friction between the Prime Minister and the Chancellor of the Exchequer over Gordon Brown's biography will stiffen Mr Blair's determination to play his full role as First Lord of the Treasury.
There is growing concern in Cabinet that control over the economy is being too tightly held by Mr Brown, and is being pursued as part of an agenda that does not always mesh with that of the Government as a whole.
It has been pointed out that in the eight months since the election, the Cabinet's economic affairs committee (EA), chaired by Mr Brown, has met fewer than half a dozen times.
Much of its business is conducted through bilateral correspondence between the Chancellor and ministerial colleagues, with copies sent to members of the EA. That process does not allow debate, and ministerial concerns are being increased by reports that they are not the only people being excluded - senior Treasury officials, too, are complaining that they are also being barred from the policy-making process.
Mr Blair has recently made three moves at the centre that could strengthen his own base in dealings with the Treasury.
Sir Richard Wilson, former Permanent Secretary at the Home Office, this month replaced Sir Robin Butler as Secretary of the Cabinet and Head of the Home Civil Service; the Strategic Communications Unit has started work at No 10, increasing the two-way flow of information between the Prime Minister's office and all departments; and a Treasury official, Jeremy Heywood, has been appointed Mr Blair's economic and domestic policy secretary - one of a strong team of private office staff led by John Holmes, the Principal Private Secretary.
Mr Blair is said to have the highest respect for the team that is now being built up: Sir Richard - a constructive mandarin who means it when he says "Yes, Prime Minister" - is attending far more meetings than Sir Robin did; the policy unit, led by David Miliband, is said to be delivering a superb product; and the Cabinet Office team, particularly Brian Bender, the European expert, have also impressed Mr Blair.
But Mr Blair's key problem remains his relationship with Mr Brown, whom he has over-ruled on a number of occasions since May; not least in ordering a Commons statement ruling out single currency membership before the next election; forcing him to disgorge an extra pounds 300m to avert a winter crisis in the NHS; and in excluding him from a lead role in welfare reform.
At last Thursday's Cabinet, Mr Blair talked of the importance of ministers sticking together - but only in the context of Jack Straw's problems with his son. He also urged ministers to give their public support to the Millennium Dome.
Few of the ministers present will have been unaware of the fact that Mr Brown's closest colleagues have been saying for weeks that the Chancellor opposes the project, if only because it is controlled by Peter Mandelson, minister without portfolio and the man he still blames for backing Mr Blair's bid, as opposed to his own, for the leadership in 1994.
For the moment, Mr Brown's simmering dispute with Mr Blair remains just that. However, if Mr Brown and his closest colleagues continue to operate outside the No 10 loop Mr Blair can be expected to take firm action.
There is no talk of the Prime Minister dropping the Chancellor but if Mr Brown pushed his luck too far, for too long, that could not be ruled out.Reuse content