Residents of the area also told Aljazeera on Wednesday that British soldiers had opened fire on civilians in the southern Iraqi town of al-Majar al-Kabir, near the British-occupied city of Basra.
Among the injured were two children and four women.
Witnesses in the area told Aljazeera that British troops had agreed with prominent local figures not to enter the town in search of weapons because they would hand them over.
However, residents said British troops launched raids late on Tuesday, aggressively searching homes. Iraqis protesting against the operation were fired upon by British soldiers.
Residents then returned fire, killing six British soldiers.
The British forces later claimed to have fired plastic bullets.
Our correspondent said tensions in the area are high and journalists were prevented from filming in the town.
In a separate incident, a British patrol in al-Majar al-Kabir came under rocket-propelled grenade attack, wounding eight British soldiers.
Three of the eight wounded soldiers were seriously injured.
Earlier, British Defence Secretary Geoff Hoon said in an emergency statement to parliament on Tuesday that the incidents had taken place at roughly the same time.
It was the first known fatal clash involving British troops since US President George Bush declared an end to hostilities on 1 May.
At least 52 American soldiers have been killed in resistance attacks since then.
US military officials on Tuesday said there had been 25 resistance attacks on occupation forces over a period of 24 hours, including an attack in al-Ramadi which left two US troops wounded and four Iraqi civilians killed.
US Defence Secretary Donald
Rumsfeld said he did not know if
there were casualties in the attack
Meanwhile, Iraqi Ahmad Hamad told the Washington Post his sister-in-law and her one-year-old child were killed in the US attack on a convoy, allegedly carrying high-ranking members of former Iraqi President Saddam Hussein's government last week.
A US rocket slammed into a residential home near the Syrian border in the village of Dhib, whose residents rely on livestock for their livelihood.
Hamad said US forces struck four trucks used to carry livestock along the border.
US military officials insisted they had "very good intelligence" and that the attack was aimed at a convoy carrying high-ranking Iraqi officials.
US Defence Secretary Donald Rumsfeld said on Tuesday he had no reason to believe that senior Iraqis were killed in the attack.
Washington said it was discussing with Damascus how to return five Syrian border guards, injured in clashes with US troops during the strike.
Rumsfeld indicated that Washington was in contact with Damascus over the incident. Syria, which lacks strong ties with Washington has not yet made a public comment.
In other developments, an American soldier died in what the US Central Command described as a "noncombat incident" in Iraq. The incident is under investigation.
Also, Britain's Daily Mirror newspaper reported on Wednesday that US troops had arrested former Iraqi Information Minister, Muhammad Said al-Sahaf, at a roadblock in a Baghdad suburb.
There was no independent confirmation of that story.