A giant column of smoke could be seen rising into the air around the city's Pul-e-Charkhi Road.
The attack was the work of a 'suicide attacker on a motorcycle' and had deliberately targeted 'foreign vehicles', General Mohammad Ayub Salangi, the country's Deputy Interior Minister, told reporters.
Kabir Amiri, a Kabul hospital chief, told AP at least five Afghan civilians had been killed and up to 34 wounded.
Khaama Press, an Afghan news website, said at least four people had been killed and at least twenty people injured.
The Taliban group claimed responsibility for the bombing, the agency added.
The number of British embassy staff hurt and the extent of their injuries was not immediately clear.
'A British embassy vehicle was attacked. There are some injuries. We are working with Afghan authorities,' a spokesperson for the British embassy told AFP.
Kabul has been the setting for a string of recent attacks on military convoys and residential compounds that are home to foreign workers.
Photographs of the attack site showed civilians walking past the mangled wreckage of at least one vehicle.
07.34 This is the latest from the Foreign Office.
We can confirm that a British Embassy vehicle has been attacked in Kabul. A number of staff have been injured.
We are working with the Afghan authorities to establish details of the incident.'
07.32 Here is what we know so far:
A suicide bomber struck a British embassy vehicle in Afghanistan's capital on Thursday and there are some casualties, a spokesman for the embassy in Kabul said.
The extent of the casualties was still unclear, officials said.
'I can confirm it was a British vehicle and there are some injuries. We are working with the Afghan authorities,' said the spokesman, who asked not to be identified.
The attack is the latest in a wave of bombings to hit Kabul as the majority of foreign combat troops withdraw from Afghanistan by the end of the year.
General Ayoub Salangi, the Afghan deputy interior minister, said the bomber was riding a motorcycle.
The blast was powerful enough to wound 33 Afghan bystanders and destroy three cars nearby, Interior Ministry spokesman Sediq Sediqqi said.
07.30 Good morning, and welcome to our live coverage of the breaking story of an attack on the British embassy in Kabul.
Entities 0 Name: Kabul Count: 6 1 Name: Afghanistan Count: 2 2 Name: British Embassy Count: 1 3 Name: Pul-e-Charkhi Road Count: 1 4 Name: Interior Ministry Count: 1 5 Name: Sediq Sediqqi Count: 1 6 Name: AP Count: 1 7 Name: Taliban Count: 1 8 Name: Foreign Office Count: 1 9 Name: Mohammad Ayub Salangi Count: 1 10 Name: Kabir Amiri Count: 1 11 Name: Khaama Press Count: 1 12 Name: AFP Count: 1 13 Name: Ayoub Salangi Count: 1 Related 0 Url: http://ift.tt/1vanjX5 Title: Exclusive: U.S. to leave more troops in Afghanistan than first planned - sources Description: Credit: Reuters/Omar Sobhani 1 of 2. U.S. troops stand guard in front of a police medical warehouse in Kabul, August 27, 2014. Picture taken August 27, 2014. The final numbers are still being agreed, but there will be at least several hundred more than initially planned, one of the sources said.
