The British military always knew the test would come and it has arrived with the offensive that Iraqi forces have launched in Basra against the Shi’ite militias and criminal gangs who have run too much of the city for too long. British-trained Iraqi units have been in action, directed by Nouri al-Maliki, the prime minister, in what is clearly a crucial encounter for the future of Iraq.

The object of the British exercise since 2003 has been to train Iraqi forces and hand control to them as soon as possible. If the strategy is seen to work then whatever follows this battle of Basra might fairly be regarded as the responsibility of the Iraqis themselves and the British will have taken a big step towards final withdrawal.

Maliki is taking a stand on his ability to exert central government authority over the increasingly lawless second city of Iraq. If the British seemed to acquiesce too easily in the slide into lawlessness in the four years they controlled Basra, a victory for Iraqi forces now would demonstrate the wisdom of being patient and letting the Iraqis run the country in their own way.

It would also be a powerful rejoinder to American mutterings that the British delude themselves into thinking their approach is sophisticated when it is simply permissive. This battle of Basra, say British military spokesmen, is what we have been working for.

If only it were that straightforward. In the coming days the Iraqis will do most of the fighting, but the British will do all the worrying. The operation looks like a dramatic test of our post-imperial approach to foreign interventions.

It is what we are trying to do in Afghanistan. It comes with the legacy of two centuries of experience in training local armies to enforce rules and conventions that we lay down. It is at the heart of the Blairite doctrine of “liberal interventionism” that justified British involvement in Iraq and Afghanistan, not to mention Kosovo, Sierra Leone or Bosnia. We are not so ideologically committed to establishing western-style democracies in failed states. A friendly and effective government, less outrageous than whatever it replaced, will normally do and we train local forces to uphold its authority.

This is primarily why Britain and the United States have been fighting different wars in Iraq since they crossed the start line in March 2003. America’s war will go on. Britain’s war may in effect end with a victory for Iraqi forces in and around Basra. Nevertheless, there is a lot to be worried about before then. If this was the battle the British military have been working for, they did not want it now.

General Mohan, commander of the Iraqi 14th Division in Basra - the unit at the heart of the fighting - may have been planning an operation like this for later in the year but Maliki summarily arrived in Basra, swept Mohan aside and started it immediately. General David Petraeus, the US commander, had merely hours’ notice of the operation, the British none at all. Far from acting under British advice, Maliki has done his best to ignore UK commanders and is working with the US corps commander at his side.

The British are delivering supplies and ammunition to Iraqi fighting units on the outskirts of the city, operating medical facilities for them and helping to provide air cover. They are struggling to avoid the consequences of having been largely swept aside by a headstrong Iraqi prime minister taking a huge personal gamble.

No surprise, then, that the operation got off to a wobbly start, that large numbers of Iraqi police either changed sides or deserted, or that a prime minister suddenly discovered he was less good at being a military commander than military commanders are.

The British will swallow their pride if it works, but there are some unpleasant implications if it does not. The Iraqi army is unlikely to be defeated in this battle. The 14th Division is well trained, as is the 10th Division in the outlying areas, and control of the air-space offers huge tactical advantages. The main objective of the operation, the Mahdi Army militia, has proclaimed itself willing to negotiate. Maliki may have calculated correctly that this particular Shi’ite militia has reached a tipping point through its inability to control its own extremists and splinter groups and has forfeited public support in Basra. All this is in Maliki’s favour. The danger is not defeat for the Iraqi army, but lack of a clear victory.

If there is a stalemate, or a battle of attrition between army and militias, there will almost certainly be another humanitarian emergency in Basra as the temperature climbs during the summer. Then the British are liable to be drawn back in - the “handing over” argument will not wash in the face of more innocent suffering and the disengagement strategy will be in disarray.

Would the British contemplate large-scale intervention to prevent a stalemate developing? In truth, there is little the 4,000 of them could do to stop it, given the 30,000 Iraqis deployed and anything up to 20,000 militias, criminals and locals prepared to oppose them. The British could mount some rescue missions, as required, but if the Iraqis cannot tip the balance themselves, only US forces have the numbers to make a decisive difference. If that proved necessary it would be difficult to discern any effective strategic purpose in Britain’s Basra occupation at all.

Herein lies the central challenge for post-imperial interventions in the present era. The British are good at adapting their military tactics to the sensitivities of different streets, good at training local forces and administrators, good at buying off all those biddable parts of insurgent movements - whether tribal leaders in Iraq or Taliban sympathisers in Afghanistan.

After the disastrous loss of the American colonies Britain built its empire, and its Commonwealth, on setting the rules, deploying few forces of its own and chancing its arm that it could keep order everywhere in a territory by demonstrating that it could keep order anywhere. It could do this only by having real influence at the political centre. In Iraq and Afghanistan that has never been the case.

The multinational interventions of today create a political nightmare of coordination and control at the highest levels. After a year or so of involvement in a failed or defeated state the international forces become part of the problem. Local leaders need to assert their authority. President Hamid Karzai of Afghanistan performs a U-turn in agreeing, then vetoing, Lord Ashdown’s appointment as central co-ordinator for the country. Maliki cannot snub his American backers but he can ostentatiously override the junior partner in the coalition.

Maliki’s high-handedness was part of his own political manoeuvring as the Shi’ite community shares out the available power. That is why the Mahdi Army and the government are negotiating. This would not matter - indeed could be welcome - if Britain could influence the political centre as it would have done in colonial days. Without that influence, a small military presence can only ever be a sideshow.

British forces can win all the tactical battles they like (as they have generally done in Iraq and Afghanistan), but if Britain lacks meaningful influence at the strategic level - even worse, if the strategy at the highest level has been confused (as it has also generally been in Iraq and Afghanistan) - then tactical victories count for little.

The battle of Basra will sharpen calls for an official inquiry into the whole Iraq venture. There will be one eventually, although it cannot tell us anything significant that we do not know. It will doubtless justify some I-told-you-so analyses and offer a checklist of warnings for a future occasion.

To be valuable, such an inquiry should weigh up the risks of Britain using its tactical military skills, with small forces, in the service of ambitious and ambiguous strategic objectives over which it cannot have more than a joint international influence. That, at least, would help to explain why the British are so much a hostage to fortune in Basra.

Professor Michael Clarke is director of the Royal United Services Institute. His work on Iraq is included in War Without Consequences, published on April 9

Martin Ivens returns next week

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