There is "insufficient material" to prove that British soldiers unlawfully killed Iraqi civilians following a vicious battle in 2004, lawyers for families of the alleged victims told a British public inquiry on Thursday.

The Al-Sweady Inquiry is investigating claims that British troops committed abuses in the aftermath of a notorious firefight near the town of Majar al-Kabir, southwest Iraq, that came to be known as the "Battle of Danny Boy" after a nearby checkpoint.

Troops had been accused of unlawfully killing 20 or more Iraqis at Camp Abu Naji near Majar-al-Kabir in May 2004 after they were taken prisoner following the battle, which was triggered when Iraqi insurgents mounted an ambush.

But following a year of evidence from 281 witnesses, at a cost of more than �22 million ($36.3 million, 26.3 million euros), lawyers for the claimants told the London hearing there was no evidence that British soldiers had carried out unlawful killings.

"Following the conclusion of the military evidence and current state of disclosure by the Ministry of Defence (MoD) it is our view there is insufficient material to establish that Iraqi civilians were unlawfully killed whilst in the custody of British troops at Camp Abu Naji and we have advised the Inquiry of this conclusion," said a statement from Public Interest Lawyers.

However, the lawyers stressed there were "numerous allegations of violent and other ill-treatment of Iraqi Civilians in British custody which the Inquiry will have to consider."

The MoD, which had strenuously denied the allegations, said it was "pleased" by the admission.

"We have long said that there was no credible evidence for these allegations and are pleased that they have been withdrawn," said a spokesman.

British army officials had dismissed the claims as "baseless rumours".

"I did not believe any of our soldiers had mutilated a body and I did not see at the time, and have not seen since, any evidence to support this proposition," Colonel Adam Griffiths told the inquiry.

He suggested that the rumours sprang from "ignorance amongst the local population as to the traumatic injuries that can be suffered in combat" as well as insurgents' efforts to discredit the US-led troops that had invaded Iraq in 2003.

Some of the bodies had broken limbs as well as gunshot wounds, Griffiths said, but he believed those injuries could have been caused by ammunition.

He suggested the unusual order to take bodies back to the camp might have been given to help identify a suspect in the murder of six British military policemen the year before.

The Inquiry -- named after one of the dead men, 19-year-old Hamid Al-Sweady -- was set up in 2009 and has been hearing testimony since March 2013.

It is the second probe into the abuse allegations, after high court judges ruled that an earlier investigation by the Royal Military Police was inadequate.

Inquiry chairman Thayne Forbes, who is due to release his final report in November, commended the lawyers "for the courage that you have displayed in making this statement at the stage that you did."