The UK’s rescue mission in Kabul is entering its final phase as troops prepare to remove Britain's military presence by August 31.
Ministers have indicated the civilian rescue will have to wrap up before then so the armed forces can withdraw troops and equipment.
European leaders failed to persuade US President Joe Biden to extend the deadline during an emergency G7 summit on Tuesday.
UK Prime Minister Boris Johnson said 10,291 people have been flown out of Kabul since August 13, more than half of them Afghans and their families.
Diplomatic staff are processing visas for Afghans entitled to travel to Britain after working for Nato troops.
Some of the people who are yet to leave Kabul are families whose rights to travel to Britain are unclear, said Foreign Secretary Dominic Raab.
“What remains are rather complex cases, large family units where one or other [person] may be documented or may be clearly a national, but it’s not clear whether the rest of them are,” he told Sky News.
Nato troops have been securing the airport since the Taliban took control of Kabul, where chaos has broken out as people try to flee. But there is no prospect of UK troops staying without the US.
Mr Biden said there was a risk of Taliban co-operation breaking down if the evacuations drag on.
He raised the threat of attacks by an ISIS affiliate in Afghanistan known as ISIS-K, which he said was seeking to target the airport and Nato troops.
The Taliban described the deadline as a red line and told of consequences for Nato countries if they did not withdraw by then.
Mr Raab said the UK military was drawing up plans for when evacuations would have to end so troops can leave by August 31.
“We’ll work to the end of August, but we’ll take back from that the time that we need to withdraw our military operation,” he said.
“The military planners are firming that up. We want to make sure we use every last hour and day to keep this rate up.”
Western leaders are urging the Taliban to allow civilian flights out of Kabul after the deadline.
Johnson's cash offer
Although they have not formally recognised the Taliban, Nato governments are holding operational contacts with them while evacuations take place.
Mr Johnson said G7 countries would use their political and economic leverage to keep the Taliban to its promises.
He suggested Afghan money frozen in foreign accounts could be released if the Taliban meets the G7’s demands.
These include preventing terrorists from using Afghanistan as a safe haven and ensuring the rights of women and girls.
Mr Johnson said the “number one condition” was to ensure safe passage for people leaving Afghanistan, including after August 31.
“If those huge funds are going to be unfrozen eventually for use by the government and the people of Afghanistan, then what we’re saying is Afghanistan can’t lurch back into becoming a breeding ground of terror, Afghanistan can’t become a narco-state, girls have got to be educated up to the age of 18, and so on,” he said.
“We want to help with the humanitarian crisis, the difficulties that people in Afghanistan and people fleeing Afghanistan are going to experience. But when it comes to engaging with the Taliban… the G7 has huge leverage.”