One of Sabiha Khudur Talib's sons claims British soldiers were involved in "torturing" and "executing" the grandmother in 2006.
Police in the Iraqi city of Basra reportedly concluded that the woman's body was dumped on a roadside in a British body bag and documents detailing their findings are to be passed to British ministers, The Independent newspaper said.
The newspaper reported that police had established there was a bullet hole in her abdomen and her face bore injuries consistent with torture.
The MoD confirmed the woman was shot by British troops when she was caught in crossfire, but deny she was murdered or tortured.
Her family say the house was raided in the early hours of November 15, 2006 and they saw Talib being led away live by soldiers afterwards.
Another of her sons, Karim Gatii Karim Al-Maliki, reportedly fired a rifle into a ceiling to scare off what he believed were criminal intruders and he was killed when the soldiers fired into the house.
Lawyers for the family demanded a full inquiry.
Phil Shiner, of Public Interest Lawyers, told The Independent: "The possibility that British forces in 2006 could have tortured and executed an innocent elderly woman should shock the nation.
"Such an allegation must be immediately independently investigated as a possible murder."
The case is one of 47 claims of abuse and torture lodged by Iraqis represented by Shiner which are being investigated by the British government.
A spokesman for the MoD said: "A post-incident report from 1st Battalion the Princess of Wales' Royal Regiment (1PWRR) describes an incident on 15 November 2006 in which soldiers from the unit were conducting an arrest operation when an Iraqi national, Karim Gatii Karim, opened fire on them.
"One British soldier was wounded and Karim Gatii Karim was shot dead. Mr Karim's mother, Sabiha Khudur Talib was regrettably wounded in the crossfire and, despite attempts to save her, she sadly died of her wounds.
"She was not tortured by British Forces and her body was not dumped by the roadside, it was returned to Iraqi authorities.
"The Royal Military Police will be investigating allegations made by Mr Karim's brother and attempting to ascertain exactly where Sabiha Khudur Talib was treated and by whom she was pronounced dead."
The spokesman added: "120,000 British troops served in Iraq and the vast, vast majority conducted themselves to the highest standards of behaviour, displaying integrity and selfless commitment."
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