The first point to note, is that, as the prime minister himself said in his statement to the House of Commons, the British troop presence in Iraq - unlike the US - has been on a steady downward trajectory since the initial phase of the war ended in May 2003. At one point total UK military personnel in the region numbered close to 40,000. By the end of 2004, the number stationed in the UK-command sector of Iraq - around Basra in the southeast of the country - was just over 9,000. Two years ago it was reduced to the current level of roughly 7,100. With yesterday's announcement , the new total will be about 5,500.

This is, obviously, well below the 150,000-plus troops the US will have in Iraq once the new counter-insurgency strategy is fully under way but it is still a long way ahead of the next largest contingent of the coalition, Poland at around 2,000. It hardly represents a retreat or a surrender, still less an abandonment of the US.

Second, the task facing the British forces in and around Basra has always been rather different from the challenge facing the US forces elsewhere. Basra is ethnically and religiously largely homogeneous - more than 80 per cent of the population is Shia Arab. For some time now the main source of violence in Basra has been twofold - extremist Islamist groups attacking British forces; and, much more important, intra-Shia Arab conflict - some of it political, some of it, simply criminal.

British commanders have known for a while that their main job was to equip and train Iraqis to deal with the internal threat. The municipal authorities in Basra may not be everybody's cup of tea, a little theocratic for my tastes, certainly - but it's nonsensical to claim that a few thousand British troops can seriously alter that.

There is still an important role for the British to play in ensuring border security in the waters of the Shatt-al-Arab and leading raids on insurgents and criminal groups as they did this month with the successful Operation Sinbad. But if the Iraqis who now run Basra can take care of security then the remaining task for British forces is to provide them the support they need - and then get out of the way.

A third, and overlooked point, in all this is that Britain has been playing an increasingly important role in the fight against terrorism in Afghanistan. Britain currently leads Nato's International Security Assistance Force and has more than 3,000 troops taking on al Qaeda and Taleban forces in the south of the country.

British forces there are dangerously stretched - a state of affairs that led recently to the disastrous decision by a British commander on the ground to hand over control of one neighbourhood to a Taleban leader. Blair's government is currently struggling to meet US requests that it add more much-needed forces to the fight in Afghanistan trying. Reducing the British footprint in Iraq will surely help.

There is, it is true, a strong element of political calculation in Blair's decision. With just a few months left in office he is eager to produce some evidence of progress in his Iraq policy. The establishment of stable democratic government in Iraq is largely out of his hands - it might even be beyond America's abilities. But with a drawdown of troops he can at least point to a limited achievement.

But even this political consideration is not to be derided. Gordon Brown, Mr Blair's probable successor, is expected to take over as prime minister this summer. He is already under pressure to make a bold statement of his foreign policy intentions by pulling British troops out of Iraq. Blair's move this week helps relieve some of that political pressure for action by a Brown government.