Britain said Friday that it planned to complete its airlifts out of Afghanistan "in a matter of hours", but that it would "shift heaven and earth" to get people out after the August 31 deadline.
"We will process those people that we have brought with us, the 1,000 people approximately inside the airfield now," British Defence Secretary Ben Wallace told Sky News, as the frenzied evacuation effort out of Kabul airport draws to a close.
"And we will seek a way to continue to find a few people in the crowd, where we can, but overall the main processing has now closed and we have a matter of hours."
Prime Minister Boris Johnson later said Britain would do everything possible to get out anyone stuck in Afghanistan after the current operation ends.
"Of course, as we come down to the final hours of the operation there will sadly be people who haven't got through, people who might qualify.
"What I would say to them is that we will shift heaven and earth to help them get out, we will do whatever we can in the second phase."
Foreign minister Dominic Raab on Friday confirmed that two British nationals and the child of another British citizen were killed in Thursday's bomb attack at Kabul airport.
"I think what their loss really underlines is the urgency of getting on and concluding Operation Pitting in the way that we are, and also underlines the bravery of our armed services, our troops, everybody else involved," Johnson said of the British casualties.
- 'Sad fact' -
Wallace earlier said that the UK had "closed the Baron Hotel" at 0330 GMT, where those wanting to fly to Britain had gathered.
It also closed the processing centre for asylum-seekers, and shut Abbey Gate, one of the points of access to Kabul airport.
Nearly 14,000 British citizens and Afghans had been rescued as part of the UK evacuations since mid-August when the Taliban swept to power, Wallace said, but added: "The sad fact is not every single one will get out".
He told LBC radio that there could be "approximately 100 to 150 British nationals left" in Afghanistan, some of them staying willingly.
He added that between 800 and 1,100 Afghans who were eligible for relocation under the UK's scheme "didn't make it".
The Times reported that documents with contact details of Afghan staff and job applicants were left lying on the ground at Britain's Kabul embassy compound.
A reporter who called the numbers found that some of those named were still in Afghanistan earlier this week and so risked reprisals.
Wallace told LBC that he learnt of this from the front-page report and "clearly it's not good enough".
"I think the prime minister will be asking some questions," he added.
The twin suicide bombs ripped through crowds outside Kabul airport on Thursday, killing at least 85 people including 13 US troops and deepening panic in the final days of the evacuation effort.
The bombings, claimed by the Islamic State group, left scenes of carnage outside the airport where thousands of Afghans desperate to flee their country had massed.
Wallace said that the "horrendous" attacks "didn't hasten our departure.
"We closed the Baron Hotel almost exactly on schedule. The threat is obviously going to grow the closer we get to leaving."