British troops executed as many as 20 Iraqi prisoners after a gun battle in May 2004, lawyers claim.
British soldiers have been in Iraq since 2003
Some alleged survivors of the gun battle near the southern Iraqi town of Majar al-Kabir also claim corpses were mutilated by UK military personnel.
Solicitor Phil Shiner said: "We would be very surprised if [the evidence] did not shock the nation."
All claims of any kind of abuse by British troops have been strongly denied by the Ministry of Defence.
The allegations were first reported a month after the fighting but lawyers acting for the survivors said this was the first time full details had been published.
At a London press conference, lawyers Mr Shiner and Martyn Day suggested prisoners taken after the three-hour gun battle - known as the Battle of Danny Boy after a checkpoint - were moved to a British base at Abu Naji and killed.
They have published written statements from five alleged survivors - Hussein Jabbari Ali, Hussain Fadhil Abass, Atiyah Sayid Abdelreza, Madhi Jassim Abdullah and Ahmad Jabber Ahmood - describing what they heard while in detention.
They say they heard other men screaming, moaning in pain and choking and also the sound of gunfire.
They also say they were cuffed and forced to wear blacked-out goggles.
The lawyers are bringing a damages claim in the UK courts on behalf of the five men and the families of the deceased.
Mr Abdelreza's statement said: "I believed people were being killed. I have never heard anything like that sound ever before in my life.
"It shocked me and filled me with such terror."
The lawyers say the five witnesses are labourers from Majar al-Kabir with "absolutely nothing" to do with the insurgent Mehdi army, who engaged British troops at the Battle of Danny Boy.
Showing images of corpses from the battle, Mr Day said: "The nature of a number of the injuries of the Iraqis would seem to us to be highly unusual in a battlefield.
"For example, quite how so many of the Iraqis sustained single gunshots to the head and from seemingly at close quarter, how did two of them end with their eyes gouged out, how did one have his penis cut off [and] some have torture wounds?"
Both lawyers are calling for the current investigation by the Royal Military Police (RMP) to be taken over by Scotland Yard.
"There is the clearest evidence available of systematic abuse and systematic failings at the very highest levels of politicians, the civil service and the military," said Mr Shiner.
Mr Day was previously involved in legal action launched against the MoD over allegations by more than 200 Masai women in Kenya that they were raped by British soldiers in the 1970s.
Mr Shiner acted for the family of Baha Mousa, an Iraqi civilian who died in British army custody in Basra in 2003.
Mr Shiner acknowledged that the bulk of the evidence relied on the five men's interpretation of what they heard while blindfolded and that no post-mortem examinations had been carried out on the bodies of the 20 dead.
But he said he believed his clients were telling the truth.
"It may be that none of this happened," he said. "We need a public inquiry to establish the facts."
An application for a High Court judicial review of the Ministry of Defence decision not to stage an inquiry had been lodged, he added.
The BBC's Panorama programme has spent more than a year talking to battlefield survivors, medical staff and Iraqi former prisoners examining the claims.
A spokesman said the programme had concluded the evidence was strongest that prisoners were mistreated.
It had seen no proof that Iraqi prisoners had died at the hands of their British captors at or after the Battle of Danny Boy.
An MoD spokesman said a 10-month Royal Military Police investigation into allegations of mistreatment, unlawful killing and mutilation by British troops had found no evidence to support them.
He added: "New allegations are part of an ongoing RMP (Special Investigation Branch) investigation and judicial review and it would be inappropriate to comment further."
Panorama: On Whose Orders? will be shown on BBC One at 20.30 GMT on Monday 25 February.