Officials of the NATO-led International Security Assistance Force (ISAF) said the twin blasts took place on Wednesday outside the UK and German military camps.
"Initial reports indicate one of our British comrades lost his life and there were several injuries," Major-General Andrew Leslie said.
Witnesses said at least four British soldiers had been wounded in the blast at the UK military camp.
"I saw four wounded soldiers and one of their Afghan translators being carried away from the car that exploded," a witness said.
The explosion occurred a day after another explosion set off by a human bomb killed a Canadian soldier and an Afghan civilian elsewhere in the city.
Wednesday's blasts are the latest in a series of attacks on international peacekeepers in trouble-torn Afghanistan.
Recent months have witnessed a sharp rise in the number of attacks, fuelling speculations the Taliban- ousted from power by US-led forces in December 2001 - and remnants of the al-Qaida are regrouping in Afghanistan's mountainous countryside.