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The UK said on Tuesday that it has flown about 8,458 people out of Afghanistan since 13 August.
It said the evacuation process would run as long as the security situation allowed and that no date was set for the end of flights.
The British Ministry of Defence said more than 1,000 Armed Forces personnel were stationed in Kabul.
Those flown out include embassy staff, British citizens, people eligible under the Afghan Relocation and Assistance Policy programme and citizens from partner countries.
British Prime Minister Boris Johnson and US President Joe Biden agreed on Monday to work together in ensuring all those eligible to leave Afghanistan were able to, including after the initial evacuation phase ended, No 10 Downing Street said.
The Taliban seized power this month from a US-backed government, sending thousands fleeing and potentially heralding a return to the militants' austere and autocratic rule of two decades ago.
Foreign Secretary Dominic Raab said at the weekend that Britain would have to turn to Russia and China to exercise a "moderating influence" over the Taliban, despite mistrust between the UK and those governments.
