Further flights which leave will have UK conciliatory and military staff ready, it added.
The top of the military, Gen Sir Nick Carter, said it was “tragic” they had not had the option to save everyone.
He said many Afghans qualified to go to the UK stayed in Afghanistan.
A mass carrier has been in progress since the Taliban assumed responsibility for the capital, with a cutoff time of 31 August set up for unfamiliar soldiers to leave the country.
The US has been running the air terminal in Afghanistan’s capital, where a self-destruction bomb assault on Thursday might have killed upwards of 170 individuals – including two British nationals and the offspring of the British public.
Among those killed in the attack was Mohammad Niazi – a taxi driver from London – who had traveled to Afghanistan to help his family get inside the airport.
It has not been confirmed whether he was one of the UK nationals referred to by the Foreign Office.
His brother Abdul Hamid said Mr. Niazi had been killed during the firing in the aftermath of the blast. He said his wife and two of his children were still missing.
Kabul airport attack: What do we know?
British nationals killed in the airport bombing
‘Taliban killed my brother for protecting my family’
More than 1,000 UK troops were in Kabul helping to process departures at the airport at the height of the operation. Some have already left and the rest will depart over the weekend.
The British ambassador to Afghanistan, Sir Laurie Bristow, who remained at Kabul airport, tweeted that nearly 15,000 people had been evacuated but it was “time to close this phase of the operation now”.
He added: “But we haven’t forgotten the people who still need to leave. We’ll continue to do everything we can to help them.”