A British daily, The Guardian, reported the allegations in its Monday edition, citing death certificates issued by the town's hospital.
Of the 22 certificates issued by hospital director Dr Adil Salid Majid, a copy of which was obtained by the newspaper, seven reported signs of "mutilation and torture".
Majid told the newspaper: "On 15 May, the police came and asked us to send ambulances to the British base to collect some bodies.
"When they brought the 22 bodies, it was a surprise to us to see some of these bodies mutilated and tortured."
The daily gave details of the cases. Ahmad al-Halfi, a 19-year-old casual labourer, is described as having "several bullet injuries to the body, with blueness of the left eye and a cut-wound by a sharp tool on the right arm.
In addition, there are signs of beating and torturing all over the body."
Haidar al-Lami, 21, also a casual labourer, had "several bullet injuries to the body, with mutilation of genitalia". His penis had been "severed".
Hamid al-Suadi, 19, is recorded as having "bullet wounds to the neck and the foot. There are signs of torture: the right arm is fractured and there is full distortion of the face."
Another, Ali al-Jamindari, 37, had "several bullet injuries in head, face and the body, with slash marks on the neck. The right arm has been severed at the shoulder. There is a large opening in the right cheek and the removal by gouging of the right eye."
Haidar al-Lami, 21, also a casual labourer, had "several bullet injuries to the body, with mutilation of genitalia". His penis had been "severed"
Dr Adil Salid Majid,
"There was an angry crowd of relatives outside the hospital gates, so we examined the bodies at once and organised the death certificates," said Majid.
"We don't have a big refrigerator here so everyone took the death certificate and the body and buried their family members."
However, a doctor at nearby Ammara hospital, who was the first to see the bodies cast doubt on the claims, and a British army spokesman in Iraq called the torture allegations "absurd".
The spokesman said: "Such claims are an insult to the whole British army and an attempt to stain the image of men who are putting their lives at risk every day to secure Iraq for the Iraqis."
The 14 May fighting in al-Majar al-Kabir outside Ammara, where six British soldiers had been killed in June 2003, was particularly violent.
"We sent a clear sign that we are not going to tolerate hostile action against our people by a minority of militia forces who are intent on causing harm and preventing the progress of what we are doing," said a ministry of defence spokesman in London.