Lawyers are going to the High Court later to push for a full public inquiry into allegations made by 142 Iraqi civilians that they were abused by British soldiers in southern Iraq.
They say there was use of outlawed stress positions as well as sensory deprivation and forced nakedness.
The Ministry of Defence says it is investigating the allegations and there is no need for public hearings.
Two public inquiries have already been launched into similar claims.
The first inquiry into the death of 26-year-old hotel worker Baha Mousa in UK military custody in September 2003, began hearing evidence last July.
And last November, the MoD announced details of a second public hearing into allegations that 19-year-old Hamid Al-Sweady and up to 19 other Iraqis were unlawfully killed and others ill-treated at a British base in May 2004.
The High Court application is being made by the Public Interest Lawyers group.
Over the past few months, the lawyers have documented a mounting number of complaints.
They include allegations not just of beatings but also of sexual humiliation and abuse. Some of the Iraqis allege they were mocked after being forced to undress and a number say they were kept awake by the playing of pornographic DVDs.
The complainants allege that at various times and in different UK facilities within Iraq between March 2003 and December 2008 soldiers and interrogators subjected them to "torture and to cruel, inhuman and degrading treatment".
Their lawyer Phil Shiner said: "This case raises a number of very troubling systemic issues about the practices and techniques used on Iraqis.
"The question for the court to decide comes down not to whether there should now be a single inquiry into the UK's detention policy in Iraq, but when it should be set up.
"Our clients are entitled to a proper inquiry into all of these cases now, not in several years time when all the evidence will be lost or forgotten."
The Ministry of Defence says it has set up a team of investigators to examine the claims which has already received at least 90 allegations.
The work is expected to take around two years because of the complexity of the investigations and the volume of allegations.
An MoD spokesman said: "These remain unproven allegations of mistreatment. The MoD takes all allegations seriously and has already set up the dedicated Iraq Historic Allegations Team (IHAT) to investigate them.
"The IHAT is the most effective way of investigating these unproven allegations rather than a costly public inquiry."