Lawyers acting for the families of some of the dead have said they are demanding improved compensation and an inquiry into the circumstances surrounding the deaths.
The British army maintains all civilians were killed either by stray bullets or when they were bystanders to operations carried out by British troops.
But the news of litigation on Sunday comes as Prime Minister Tony Blair struggles to calm a storm caused by accusations that British security services bugged the United Nations and the attorney general was pressured to give the war a legal bill of health.
The prosecution team said they had written to Defence Secretary Geoff Hoon demanding he should immediately set up an inquiry into the deaths.
But they also demand the Ministry of Defence (MoD) should accept liability for what they claim are unlawful killings and full damages to compensate the 13 families they are representing.
The MoD said it had already offered and paid compensation totalling ?15,000 ($27,800) since last May, but it did not accept liability for any of the deaths.
"It is a shock to discover that British troops have caused the deaths of so many innocent Iraqis since our occupation began on 2 May 2003"
member of Public Interest Lawyers
Phil Shiner of Public Interest Lawyers, which is pursuing the claims, said there had to be an independent inquiry and full damages paid to all the families.
"The MoD must establish a fair and rational compensation scheme so all those who have been affected by unlawful killings, injuries or loss of property, can be compensated without the stress of litigation," he said in a statement.
"It is a shock to discover that British troops have caused the deaths of so many innocent Iraqis since our occupation began on 2 May 2003."
One of the barristers acting for the plaintiffs is the well-known human rights lawyer and co-founder of Matrix Chambers - Rabinder Singh.
Between 8200 and 10,100 Iraqi civilians have died in the Iraq conflict, according to estimates by academics and peace activists.