Suicide Bombers Hit Brit Offices In Kabul
At least three people were killed in the initial attack early on Friday morning, the city's criminal investigations chief told AFP.
But a fresh explosion earlier in the morning took the death toll to at least eight. Most of the dead are thought to be police.
"Eight people, mostly police, are killed and 10 others injured," Siddiq Siddiqui of Afghanistan's interior ministry said.
"There is one person, one of the attackers who is still alive and resisting. The area has not yet been cleared."
The Times' Kabul correspondent Jerome Starkey told Sky News gun battles continued amid the bombed offices.
He said British forces at the scene had begun pushing the cordon around the building back, giving rise to fears there were still attackers inside the building.
"There were shots coming out of the wreckage of the British Council," Mr Starkey said.
"Apache helicopters have been circling around the building and the battle is still ongoing."
It is unclear if any Britons have been killed or injured in the attack.
The Taliban has claimed it launched the attack on the British cultural institution in Kabul to mark the country's independence from Britain in 1919.