The cases, to be taken to the High Court this week, aim at securing for the families their rights to be "informed of and be involved in full investigations into the deaths of their relatives".
"None of my clients has been told of, or involved in, any investigations," said Phil Shiner, the lawyer representing the families.
"Such failure falls far short of the government's obligations under the Human Right Act."
The cases involve five Iraqi civilians who were killed in shootings while going about their daily lives - after the US-led war in Iraq was officially stated to be over.
Another case involves the death of Baha Musa, an ex-hotel receptionist who died in British custody after suffering what his lawyers say were "severe beatings".
"None of my clients has been told of, or involved in, any investigations. Such failure falls far short of the government's obligations under the Human Right Act"
Phil Shiner, lawyer for the Iraqi families
Musa, 26, died in September 2003 after soldiers arrested him and seven other young Iraqis in the southern city of Basra. His battered body was returned to his family four days later.
A spokesman for the British Ministry of Defence (MoD) said it would be "robustly" defending the case.
"We have every confidence in the existing legal framework in which our armed forces are operating," he said. "The MoD will defend this position robustly."
In a preliminary hearing at the High Court in May, the Iraqi families had won the right to challenge the government's refusal to open independent inquiries into the deaths.
The lawyers for the families argue that because the Iraq war was officially over when the victims died, and because the UK was an occupying power, the European Convention on Human Rights should apply.
US President George Bush had declared major combat over on 1 May 2003.
Human-rights campaigners Amnesty International published a report in May accusing British soldiers of killing Iraqi civilians – including an eight-year-old girl - when they posed no apparent threat.