A civilian interpreter also died in the blast, while a fifth soldier was wounded.
The improvised explosive device created a large crater in the west of Iraq's second city, which has seen six fatalities among UK armed forces in the last week alone.
After prime minister Tony Blair accused Iran of supporting terrorism in Iraq and came close to specifically linking Iran to the explosion in Basra yesterday, attention has focussed on whether the British military can establish the make of explosive device used in the attack.
MoD officials say they have identified the type of explosive used but are yet to reveal this information. The commander of Basra's police forces, Major General Mohammed al-Moussawi, has said he believes the bomb to have been of Iranian origin.
2nd Lt Dyer and Pte Dlugosz are only the third and fourth female fatalities among British forces since the 2003 invasion of Iraq. Flight Lieutenant Sarah-Jane Mulvihill died in May last year when the Lynx helicopter she was travelling in crashed in Basra City, while Staff Sergeant Denise Michelle Rose was found dead in a military base in Basra in October 2004.
Britain's total death toll in Iraq rose to 140 after yesterday's deaths.
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