The UK’s last civilian evacuation flight left Afghanistan’s capital, Kabul, the Defense Ministry said.
Additional flights departing will have British diplomatic and military personnel on board, she added.
The chief of the armed forces, General Sir Nick Carter, said it was “heartbreaking” that they couldn’t save everyone.
He said hundreds of Afghans who might come to the UK stayed in Afghanistan.
Since the Taliban took control of the capital, a mass airlift has been underway, which foreign troops are allowed to leave until August 31.
The US operates the airport in the Afghan capital, where a suicide attack on Thursday may have killed up to 170 people – including two British nationals and a child of a British national.
Among those killed was Mohammad Niazi – a taxi driver from London – who had traveled to Afghanistan to help his family board the airport.
It has not been confirmed whether he was one of the British nationals named by the Foreign Office.
His brother Abdul Hamid said Mr. Niazi was killed in the shooting after the explosion. He said his wife and two of his children were still missing.
More than 1,000 British soldiers were in Kabul handling departures at the airport at the height of the operation. Some have already left and the rest will leave on 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 is time to complete this phase of the operation now”.
He added, “But we haven’t forgotten the people who have yet to leave. We will continue to do everything we can to help them. “