The evacuation mission is entering its final days and hours, as troops prepare to wind up operations and get themselves out before the Aug. 31 deadline.
About 1,000 Afghans who have been authorised to come to the UK are still estimated to remain in Kabul.
Armed forces minister James Heappey said that since Aug. 13 the UK has airlifted 12,279 people out of Afghanistan.
That includes 1,988 people on eight RAF flights in the past 24 hours.
Eleven more flights are scheduled out of Kabul today, he said.
PA news agency reported that on Aug. 25 nearly 2,000 Afghans authorised for UK evacuation under the Afghan Relocations and Assistance Policy were still estimated to be stuck in Kabul.
But Heappey said the number outstanding has now dropped to “potentially half” of the previous estimate.
The government has given no precise figure on how many Brits are still in Afghanistan.
UK Foreign Secretary Dominic Raab previously said that “almost all” single-nationality UK citizens who wanted to return are now out of Afghanistan.
Last-ditch evacuation efforts are currently being hampered by the threat of a terrorist attack at Kabul airport by a local ISIS spin-off group.
British and U.S. authorities have warned people not to travel to the airport, due to what Heappey described as a “very imminent” risk of a “highly lethal” attack, possibly within Kabul.
“As a consequence, we’ve had to change the travel advice to advise people not to come to the airport, indeed to move away from the airport, find a place of safety, and await further instruction,” he told the BBC.
The British evacuations are expected to end in the next day or two, or to at least dramatically drop, as the military starts to wind up its operations and withdraw ahead of the Aug. 31 deadline.
Heappey has declined to say whether today’s flights out of Kabul will mark the end of the rescue operation.
Former defence chief Lord David Richards previously told The Daily Telegraph that although rescue operations would likely end by Friday, British troops would continue to “sneak others in who arrived late along with their own people.”
The French prime minister has already announced that France will end evacuation flights tomorrow.
In the United States, Pentagon press secretary John Kirby said that evacuations can continue until the end but conceded that they will have to prioritise moving out U.S. military capability in the “last couple of days.”
He said more than 4,400 American citizens have been evacuated so far.
More than 80,000 people, mostly Afghans, have been airlifted by the United States since Aug. 14, he said.
PA contributed to this report