We have had some remarkable coalitions of opposites in English political history – Fox and North, Churchill and Attlee – none as extreme as Blair and Brown. Tony Blair has been the most theatrical of our Prime Ministers, playing the idealist with an airy charm; Gordon Brown has been the most grave of our Chancellors, conducting our finances with a barely concealed Cromwellian rage. For much of the time they have made an effective partnership, with a tendency to block each other’s mistakes. Mr Brown’s refusal to let Mr Blair take Britain into the euro is an example of that; it has proved a great national benefit.

The Granita deal divided the Government between them; defence and foreign affairs fell into the Prime Minister’s half. The euro counted as finance, so Mr Brown was able to decide that policy. Iraq was foreign affairs, so Iraq was Mr Blair’s responsibility. Mr Brown was not enthusiastic for the invasion of Iraq. He had to give the policy his support; indeed, he had to vote for it. Otherwise he would have had to resign, like Robin Cook. Yet his endorsement was reluctant and minimalist.

In a month’s time Mr Brown will be Prime Minister. There will then be no counterweight to his authority on the Labour front bench. John Reid has already said that he will retire from office. Jack Straw will be the senior figure, but neither he, nor whoever is elected deputy leader, will have the political weight to resist any of the major policies of the new Prime Minister. On Iraq, which did so much damage to Mr Blair, Mr Brown can move in the direction that he chooses.

Both men have recently been to Washington; American observers probably have a better idea of their real views than anyone else. President Bush still has every confidence in Mr Blair, the loyal ally whose retirement he regards as a serious blow. Equally, the President is suspicious that Mr Brown will change British policy, and accelerate the withdrawal of British troops from Iraq. He says that Mr Brown is a “good fella”; that is the one thing that Mr Brown is not; to British ears it sounds almost as patronising as did “yo, Blair”.

It is more than likely that the President has read Mr Brown’s mind correctly. Most of the arguments point in the same direction. Mr Brown was never enthusiastic about the invasion; the policy decision was not his and he owes no personal loyalty; the war is unpopular in Britain and in the US; it cost the Republicans both houses of Congress; the European Prime Ministers who supported the war have all left office; the British forces in Iraq and Afghanistan are overstretched; the remaining 5,500 men in the Basra air base are not nearly enough to impose order on a city of two million; the security position in Iraq is very bad and the American “surge” does not seem greatly to have improved it.

If Mr Brown does follow the logic of this argument, there is an attractive political scenario for him. In 1997 he moved decisively to give the Bank of England independence to set interest rates. That was Labour’s first smack of “firm government”. If Mr Brown takes a radical decision on Iraq, that could well leave the same impression of decisiveness. It could lift Labour in the polls, perhaps even to the point at which an autumn election became an attractive option.

There are certainly arguments on the other side. What impact would a policy of more rapid withdrawal have on oil, terror and the Arab world? Such a change of policy might leave Iraq to anarchy and outright civil war; it might also be seen as disloyal to the Anglo-American alliance – certainly President Bush would resent it. Yet there are some plausible replies to these counter-arguments. No British effort that is now conceivable would make much difference to Iraq; indeed, we might make it worse by staying. Afghanistan is a different matter; troops and equipment released from Iraq might well be useful there.

So far as the American alliance is concerned, Mr Brown would indeed be moving away from the Republicans, but he would be linking up with Labour’s natural allies, the Democrats. In terms of the withdrawal of troops, he would be going no further than the congressional Democrats have already proposed. At present the Democrats are the favourites to win the White House in November next year. The primaries will start in January. Mr Brown may be more concerned to establish a political friendship with the next President than to retain the friendship of President Bush.

All of these arguments must be in Mr Brown’s mind. My expectation is that he will move in the direction of withdrawal, but with caution. He cannot be sure who the next President will be. It would be very damaging if British troops withdrew in a way that exposed the lines of communication of American soldiers in Iraq. Britain has earned the reputation in the United States of being a loyal ally, and we must retain that. There is also a real duty to give the Iraqis the best possible opportunity to solve their own problems.

The politics may be decisive. Mr Brown wants to win another overall majority for Labour at the next general election; nothing less will do. The accelerated withdrawal of British troops from Iraq would be popular, in proportion to the unpopularity of the war. Even the generals would support it, to reduce the overstrain on the Army.

The Conservatives are at the disadvantage of all Oppositions; Governments can act, but Oppositions can only talk. At the end of Mr Blair’s long, drawn-out process of retirement, Labour has lost momentum and needs to regain it. Mr Brown has an opportunity to show that he is a decisive leader, not afraid of the anger of President Bush. He may well take that opportunity.

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