The other three killed were Afghan civilians and up to 33 others hurt, officials in the country said.
Mr Hammond also confirmed that a British national civilian security team member had been injured in the suicide attack.
‘Inhumanity’
In a statement, he condemned the “appalling attack on innocent civilians”. Mr Hammond said: “This outrage brings home to us once again the courage and perseverance of the people of Afghanistan and members of the international community who support them, who have lived together through decades of conflict.
We will not allow such inhumanity to deter us from continuing our partnership with the Government of Afghanistan. Philip Hammond
“We will not allow such inhumanity to deter us from continuing our partnership with the Government of Afghanistan. I have nothing but admiration for the staff of the Embassy, British and Afghan, who work at great personal risk to help build a better future for Afghanistan.”
General Ayoub Salangi, the deputy interior minister, said that the vehicles were targeted by a suicide attacker on a motorcycle.
Foreign Office minister Simon Fraser said he was “shocked” by the news:
Shocking news from #Kabul of attack on British Embassy vehicle. Working to get full facts. Thoughts with all our people @UKinAfghanistan.