The attack on the British Council occurred as Afghans on Friday celebrated Independence Day, marking the day the country achieved full independence from Britain in 1919.
A spokesman for the Taleban, Zabiullah Mujahid, claimed responsibility for the attack.
The dead included eight Afghan policemen, a security guard whose nationality was not immediately known and an Afghan municipal worker, according to Kabul police official Farooq Asas. Two of four people wounded in the blasts were not Afghans, he said.
The attack started with one suicide bomber detonating an explosives-laden car outside the British Council in west Kabul while another suicide bomber struck inside the compound, according to Afghan police.
Afghan security forces dispatched to the scene said that at least three insurgents fought from a secure bunker inside the compound with rifles and rocket propelled grenades.
An Afghan policeman named Azizullah said that the insurgents wrestled weapons and ammunition from the guards at the compound. Afghan men often go by one name only.
In London, the British Foreign Office confirmed that all U.K nationals were safe following the attack on the British Council.
British authorities would not say how many of their personnel were inside the building at the time of the attack. At one point Afghan police carried a man with a Union Jack patch on his shoulder on a stretcher away from the scene.
The stand-off was still going on five hours after the initial blasts.
Asas, the police official, said he had counted five suicide bombers. One detonated the car outside the compound, one set of an explosion inside while at least three more got inside the compound on foot.
Ambulances and at least one helicopter airlift ferried casualties to hospital.
The explosions shattered glass windows a third of a mile (half a kilometer) from the site.
Afghan troops led the assault on the insurgents, but NATO troops were on the scene in an advisory role.
The walled compound of the British Council is located in an upscale residential area in west Kabul. It consists of two buildings, one is a two-story building and the is other a single-story structure. The Council focuses on aiding foreign nations with education and building civil society.
Friday’s fighting damaged two neighboring high schools and several auto repair and auto parts shops nearby.
While violence continues to rage in many parts of Afghanistan, attacks in the capital are relatively uncommon. In June, 21 people were killed at a Kabul hotel, including nine insurgents, with militants fighting NATO and Afghan troops for five hours with rocket-propelled grenades and suicide bombs.
