In a dramatic blow to Defence Secretary Geoff Hoon, who had opposed a fresh investigation, two senior High Court judges ruled in favour of the family of hotel worker Baha Mousa, 26, who was allegedly beaten to death.
Mr Hoon's lawyers contended an investigation could not be held under the provisions of the European Convention on Human Rights as it did not apply to British troops in south east Iraq.
But the judges held that the UK's obligations under the European Convention on Human Rights extended to "outposts of the state's authority" in foreign lands and that included prisons operated by British troops.
Any subsequent inquiry will investigate whether there has been unlawful killing and breaches of articles 2 and 3 of the convention, which guarantee the right to life and freedom from torture and inhuman and degrading treatment.
The Mousa family could be entitled to damages from the British Government if breaches are proved.
Family lawyer Phil Shiner hailed it as "a historic day for human rights and the rule of law in the UK."
He called for the immediate appointment of a UK judge to investigate all the allegations of torture made against British soldiers serving in Iraq including the case of Baha Mousa, "the most terrible of all."
In their written judgment, Lord Justice Rix and Mr Justice Forbes were strongly critical of "the dilatoriness of the investigative process" already conducted by the Royal Military Police's Special Investigations Branch.
Making a fresh inquiry inevitable if their decision is not overturned on appeal, the judges said it was difficult to say that the SIB investigation "has been timely, open or effective."
The inquiries made so far "are not adequate in terms of the procedural requirements of Articles 2 and 3 of the Convention."
But the judges rejected applications for judicial review made by five other families of Iraqis allegedly unlawfully killed by troops in south east Iraq following the cessation of major hostilities in May 2003.
Dismissing their claims to independent investigations under the Human Rights Act, which incorporates the European convention into domestic law, the judges said the claims arose "out of shootings of Iraqis by British forces in the field."
The victims were not in custody and the deaths occurred on Iraqi territory which was outside UK jurisdiction and "outside the scope of the convention and the Act."
The judges said: "There may be other remedies, but we are not here concerned with that."
Yesterday's cases were test cases arising out of some 37 deaths of Iraqis, allegedly at the hands of British troops.
The Ministry of Defence welcomed the court's decision to reject five of the six cases but refused to comment further on the Mousa case because a prosecution in relation to it was still under consideration.
Meanwhile, Prime Minister Tony Blair's official spokesman said: "Obviously we will need to study this detailed judgment. I would point out, however, that a separate criminal case is currently being considered by the army prosecuting authority."
Some 30 other similar cases were awaiting yesterday's court ruling.
Both sides were granted permission to appeal.
Mr Shiner, who brought yesterday's challenge on behalf of Mr Mousa's father, Daoud Mousa, a colonel in the Basra police, said: "All the cases of torture by UK soldiers during the occupation of Iraq including the most terrible of all where Baha Mousa was tortured to death must now be investigated here in the UK."