A British military spokesman in London said the soldier died when two British army vehicles came under fire from resistance fighters in the southern Iraqi city .
Another spokesman on the ground said that five British soldiers were wounded in Basra.
It was not immediately clear if one of those five had subsequently died or whether the fatality was a separate incident.
A spokesman had said earlier that there were no casualties when fighters fired a rocket-propelled grenade at a convoy about 2pm (1000 GMT).
The incident occurred in the centre of the city, close to the provincial administration buildings.
Aljazeera television said the resistance has vowed to close the road between the port city of Um Qasr and Basra even as fighting continued in the city's suburbs.
Two British Land Rovers were
destroyed in the fighting
This came after Salam al-Maliki, Shia leader Muqtada al-Sadr's representative in the city and a member of the provincial authority, threatened to fight for the secession of the three southern provinces of Basra, Dhiqar and Maysan from the rest of Iraq if US troops did not withdraw from Najaf.
Another al-Sadr aide, Asad al-Basri, warned that "Basra would be turned into another Najaf" if the US military did not pull out of the holy city further north.
Resistance fighters linked to Muqtada al-Sadr have been fighting occupation forces in several southern cities and Baghdad over the past few days, with the heaviest fighting going on in the city of Najaf.