"There are credible allegations of serious, inhumane practices across a whole range of dates and facilities concerning British military detention in Iraq," Michael Fordham, representing the Iraqi group, was quoted by the PA news agency as saying.
Lawyers for the claimants are appearing at the High Court in London over three days to challenge a refusal by the UK government to hold an investigation into British-controlled detention facilities in Iraq.
The legal team submitted video evidence to the court on Friday, showing a detainees being interrogated at a secret British centre in Basra.
The claims of inhumane treatment involve sexual humilitation, keeping Iraqis naked if they did not co-operate, food and water deprivation and prolonged solitary confinement.
Ali Zaki Mousa, the lead claimant in the case, alleges he suffered months of beatings and other abuse in the custody of British soldiers between 2006 and 2007.
Another 60 other Iraqis are also making complaints against the British military, and there is speculation that more could follow.
'Getting to the truth'
The claimaints say that the abuse occurred during the period March 2003 to December 2008 in British-controlled detention facilities in Iraq.
The ministry of defence said it is taking the allegations seriously, but would not be holding a public inquiry.
"The MoD takes all allegations seriously and has already set up the dedicated Iraq Historic Allegations Team (Ihat) to investigate them," it said in a statement.
"The Ihat is the most effective way of investigating these unproven allegations rather than a costly public inquiry."
The British government has already held the Baha Mousa inquiry, which looked into specific allegations of abuse and another, the Al Sweady trial, is due to begin holding hearings next year.
Lawyers for Liam Fox, the British defence secretary, argue that those inquiries, along with the Ihat investigations, are enough to meet the UK's obligations to fully investigate under the European Convention on Human Rights.
But public-interest lawyers representing the Iraqi group say the two inquiries only cover a fraction of the cases.
They are arguing that there are so many claims that at the current pace it would take more than 100 years to hear them all.
Fordham, speaking for the Iraqi group, said the public inquiry being called for would not ignore the findings of the other inquiries but become part of an "integrated solution" to help discover the truth.
"It just means that somebody who is independent is taking responsibility for getting to the truth," he said.
Source: Al Jazeera and agencies