While the official coalition figures list the British as the second largest contingent with around 9,900 troops, they are narrowly outnumbered by the 10,000 private military contractors now on the ground.
The investigation has also discovered that the proportion of contracted security personnel in the firing line is 10 times greater than during the first Gulf war. In 1991, for every private contractor, there were about 100 servicemen and women; now there are 10.
The private sector is so firmly embedded in combat, occupation and peacekeeping duties that the phenomenon may have reached the point of no return: the US military would struggle to wage war without it.
While reliable figures are difficult to come by and governmental accounting and monitoring of the contracts are notoriously shoddy, the US army estimates that of the $87bn (£50.2bn) earmarked this year for the broader Iraqi campaign, including central Asia and Afghanistan, one third of that, nearly $30bn, will be spent on contracts to private companies.
The myriad military and security companies thriving on this largesse are at the sharp end of a revolution in military affairs that is taking us into unknown territory - the partial privatisation of war.
"This is a trend that is growing and Iraq is the high point of the trend," said Peter Singer, a security analyst at Washington's Brookings Institution. "This is a sea change in the way we prosecute warfare. There are historical parallels, but we haven't seen them for 250 years."
When America launched its invasion in March, the battleships in the Gulf were manned by US navy personnel. But alongside them sat civilians from four companies operating some of the world's most sophisticated weapons systems.
When the unmanned Predator drones, the Global Hawks, and the B-2 stealth bombers went into action, their weapons systems, too, were operated and maintained by non-military personnel working for private companies.
The private sector is even more deeply involved in the war's aftermath. A US company has the lucrative contracts to train the new Iraqi army, another to recruit and train an Iraqi police force.
But this is a field in which British companies dominate, with nearly half of the dozen or so private firms in Iraq coming from the UK.
The big British player in Iraq is Global Risk International, based in Hampton, Middlesex. It is supplying hired Gurkhas, Fijian paramilitaries and, it is believed, ex-SAS veterans, to guard the Baghdad headquarters of Paul Bremer, the US overlord, according to analysts.
It is a trend that has been growing worldwide since the end of the cold war, a booming business which entails replacing soldiers wherever possible with highly paid civilians and hired guns not subject to standard military disciplinary procedures.
The biggest US military base built since Vietnam, Camp Bondsteel in Kosovo, was constructed and continues to be serviced by private contractors. At Tuzla in northern Bosnia, headquarters for US peacekeepers, everything that can be farmed out to private businesses has been. The bill so far runs to more than $5bn. The contracts include those to the US company ITT, which supplies the armed guards, overwhelmingly US private citizens, at US installations.
In Israel, a US company supplies the security for American diplomats, a very risky business. In Colombia, a US company flies the planes destroying the coca plantations and the helicopter gunships protecting them, in what some would characterise as a small undeclared war.
In Kabul, a US company provides the bodyguards to try to save President Hamid Karzai from assassination, raising questions over whether they are combatants in a deepening conflict with emboldened Taliban insurgents.
And in the small town of Hadzici west of Sarajevo, a military compound houses the latest computer technology, the war games simulations challenging the Bosnian army's brightest young officers.
Crucial to transforming what was an improvised militia desperately fighting for survival into a modern army fit eventually to join Nato, the army computer centre was established by US officers who structured, trained, and armed the Bosnian military. The Americans accomplished a similar mission in Croatia and are carrying out the same job in Macedonia.
The input from the US military has been so important that the US experts can credibly claim to have tipped the military balance in a region ravaged by four wars in a decade. But the American officers, including several four-star generals, are retired, not serving. They work, at least directly, not for the US government, but for a private company, Military Professional Resources Inc.
"In the Balkans MPRI are playing an incredibly critical role. The balance of power in the region was altered by a private company. That's one measure of the sea change," said Mr Singer, the author of a recent book on the subject, Corporate Warriors.
The surge in the use of private companies should not be confused with the traditional use of mercenaries in armed conflicts. The use of mercenaries is outlawed by the Geneva conventions, but no one is accusing the Pentagon, while awarding more than 3,000 contracts to private companies over the past decade, of violating the laws of war.
The Pentagon will "pursue additional opportunities to outsource and privatise", the US defence secretary, Donald Rumsfeld, pledged last year and military analysts expect him to try to cut a further 200,000 jobs in the armed forces.
It is this kind of "downsizing" that has fed the growth of the military private sector.
Since the end of the cold war it is reckoned that six million servicemen have been thrown on to the employment market with little to peddle but their fighting and military skills. The US military is 60% the size of a decade ago, the Soviet collapse wrecked the colossal Red Army, the East German military melted away, the end of apartheid destroyed the white officer class in South Africa. The British armed forces, notes Mr Singer, are at their smallest since the Napoleonic wars.
The booming private sector has soaked up much of this manpower and expertise.
It also enables the Americans, in particular, to wage wars by proxy and without the kind of congressional and media oversight to which conventional deployments are subject.
From the level of the street or the trenches to the rarefied corridors of strategic analysis and policy-making, however, the problems surfacing are immense and complex.
One senior British officer complains that his driver was recently approached and offered a fortune to move to a "rather dodgy outfit". Ex-SAS veterans in Iraq can charge up to $1,000 a day.
"There's an explosion of these companies attracting our servicemen financially," said Rear Admiral Hugh Edleston, a Royal Navy officer who is just completing three years as chief military adviser to the international administration running Bosnia.
He said that outside agencies were sometimes better placed to provide training and resources. "But you should never mix serving military with security operations. You need to be absolutely clear on the division between the military and the paramilitary."
"If these things weren't privatised, uniformed men would have to do it and that draws down your strength," said another senior retired officer engaged in the private sector. But he warned: "There is a slight risk that things can get out of hand and these companies become small armies themselves."
And in Baghdad or Bogota, Kabul or Tuzla, there are armed company employees effectively licensed to kill. On the job, say guarding a peacekeepers' compound in Tuzla, the civilian employees are subject to the same rules of engagement as foreign troops.
But if an American GI draws and uses his weapon in an off-duty bar brawl, he will be subject to the US judicial military code. If an American guard employed by the US company ITT in Tuzla does the same, he answers to Bosnian law. By definition these companies are frequently operating in "failed states" where national law is notional. The risk is the employees can literally get away with murder.
Or lesser, but appalling crimes. Dyncorp, for example, a Pentagon favourite, has the contract worth tens of millions of dollars to train an Iraqi police force. It also won the contracts to train the Bosnian police and was implicated in a grim sex slavery scandal, with its employees accused of rape and the buying and selling of girls as young as 12. A number of employees were fired, but never prosecuted. The only court cases to result involved the two whistleblowers who exposed the episode and were sacked.
"Dyncorp should never have been awarded the Iraqi police contract," said Madeleine Rees, the chief UN human rights officer in Sarajevo.
Of the two court cases, one US police officer working for Dyncorp in Bosnia, Kathryn Bolkovac, won her suit for wrongful dismissal. The other involving a mechanic, Ben Johnston, was settled out of court. Mr Johnston's suit against Dyncorp charged that he "witnessed co-workers and supervisors literally buying and selling women for their own personal enjoyment, and employees would brag about the various ages and talents of the individual slaves they had purchased".
There are other formidable problems surfacing in what is uncharted territory - issues of loyalty, accountability, ideology, and national interest. By definition, a private military company is in Iraq or Bosnia not to pursue US, UN, or EU policy, but to make money.
The growing clout of the military services corporations raises questions about an insidious, longer-term impact on governments' planning, strategy and decision-taking.
Mr Singer argues that for the first time in the history of the modern nation state, governments are surrendering one of the essential and defining attributes of statehood, the state's monopoly on the legitimate use of force.
But for those on the receiving end, there seems scant alternative.
"I had some problems with some of the American generals," said Enes Becirbasic, a Bosnian military official who managed the Bosnian side of the MPRI projects to build and arm a Bosnian army. "It's a conflict of interest. I represent our national interest, but they're businessmen. I would have preferred direct cooperation with state organisations like Nato or the Organisation for Security and Cooperation in Europe. But we had no choice. We had to use MPRI."
http://www.guardian.co.uk/international/story/0,3604,1103566,00.html