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Britain's last evacuation flight could leave Kabul in five days under an accelerated timetable for withdrawal from Afghanistan, The Times newspaper reported.
Ministers were told this week that the last flight might have to leave next Tuesday before the planned departure of American troops on August 31, the newspaper reported.
But a government source was quoted as saying the Tuesday evacuation date had not yet been formally agreed to.
Britain is unable to evacuate unaccompanied children from Afghanistan, Defence Secretary Ben Wallace said on Thursday when asked about footage of a young child being handed over a wall to western soldiers at Kabul airport.
A spokeswoman for Britain's Foreign Ministry said about 1,200 people had left Kabul on flights for the UK since Sunday.
Britain is working with the Taliban in Kabul on a "tactical, practical level" to fly out citizens and eligible Afghans, Britain's ambassador to Afghanistan, Sir Laurie Bristow, said on Wednesday.
The Taliban seized power last weekend in an upheaval that sent thousands of civilians and Afghan military allies fleeing for their safety.